Britain's biggest industrial dispute in a generation has taken a significant step towards resolution after major trade unions agreed to suspend strike action while they consider proposals on public sector pension changes.

Danny Alexander, the chief secretary to the Treasury, will make a statement to the Commons on Tuesday to outline the situation as the original 31 December deadline for resolving the talks looms.

Unions representing health, civil service and local government workers agreed to consider outline deals, while talks with education representatives were adjourned and will continue in the new year, according to the National Union of Teachers.

However, the Association of Teachers and Lecturers (ATL) was the latest union to confirm that it has signed the "heads of agreement", which means that in principle, it will take the government's offer back to its members.

The ATL – one of the most moderate teaching unions – took strike action alongside two other education unions in June for the first time in its 127-year history. The union was also among the 29 unions that took part in the mass co-ordinated action on 30 November.

The largest public sector union, Unison, confirmed it would not set strike dates while it consulted on the proposals, as labour movement sources acknowledged Monday's developments headed off the prospect of a further public sector general strike in the new year. However, there was dissent from one important player, as the biggest civil service union, the Public and Commercial Services union, rejected a deal.

Speaking after talks with union leaders at the Trades Union Congress headquarters in London, the TUC general secretary, Brendan Barber, said mass walkouts were not the priority. "We have reached a stage where the emphasis in most cases is in giving active consideration to the new proposals that have emerged rather than considering the prospect of further industrial action," he said.

Last month, more than 1 million public sector workers, including teachers, social workers and immigration officials, took part in the biggest outbreak of industrial action since 1979 in walkouts union leaders said were crucial to securing progress in subsequent talks.

The PCS, whose members include UK Border Agency staff, rejected the proposals and was promptly barred from further talks. The Unite union also expressed ambivalence and said it would not be rushed into backing the outline deals, which detail the general structure of the new pension schemes, although fine details will be ironed out in further talks if unions back the proposals. A union source said reaction to the outline deals split into three groups: acceptance; a pledge to consult members; and outright rejection.

Christine Blower, general secretary of the NUT, said negotiations had been conducted in a "fairly shambolic way" from the government's point of view.

"There was some movement, but we have taken the view that there was insufficient movement," she said. Blower said that much of the documentation the NUT needed to make a decision over the offer had not been produced. "We have reserved our position. We will await all the documentation and we will discuss this with our executive early in January. We expect that if there are further negotiations we will be present at them."

The chancellor, George Osborne, was checking the costs of the proposed deals before a statement expected on Tuesday in the Commons by Danny Alexander, the chief secretary to the Treasury and a lead figure in the talks alongside the Cabinet Office minister, Francis Maude.

The new pension schemes will be career-average, but extra protections have been provided for employees with 10 years or fewer to retirement. Further talks on the scale of possible contribution increases, reaching £2.8bn by 2015, will be held separately.

Cabinet Office and Treasury officials said they had resolved some main issues without needing to increase the overall cost of the deal beyond concessions set out last month. These included changes to accrual rates, which determine the amount a pension increases each year.

Stressing that it has not agreed a formal deal, Unison said the government had made a final offer on health that would be considered on 10 January by its health committee, which would then decide whether to accept, reject or consult on the proposals. A spokeswoman said: "We have signed an agreement to discuss it with our executive, and we will not call any strikes in the meantime."

Unison, the GMB and Unite have agreed a negotiation framework on changes to the local government fund, but the accord is awaiting the formal approval of the communities secretary, Eric Pickles. A formal offer has also been tabled in civil service talks, with the Cabinet Office asking unions to secure approval from their executives on the basic outline of changes. The offer for civil servants, seen by the Guardian, consists of sections including the "main parameters" and "areas for further detailed discussion", with one union source saying that the document is essentially a deal on the framework of reforms, with finer details still to be thrashed out.

The Prospect civil service union said it would hold talks about accepting the deal with its members and its executive, with the FDA union for senior civil servants also preparing to consult members. Dai Hudd, Prospect's deputy general secretary, said: "While we will not call for further industrial action while these outstanding issues are being resolved and we are consulting members, we reserve the right to do so if the discussions fail to produce an acceptable outcome."

The PCS general secretary, Mark Serwotka, urged unions to fight the changes: "We should call further industrial action in the new year because this is so unfair, we have got to stand up against it. We are going to go and hear what the other unions have got to say. Our message really is that those unions will have to be accountable to their members for what they do. We all came out together."

Talks on education, the last remaining scheme, are taking place in Whitehall but a well-placed source said an outline agreement was also likely to emerge.

The developments do not mean an end to the public sector pensions dispute, with union sources stressing the deals need to be put to a ballot and the PCS still seeking industrial action.

Unison's head of health, Christina McAnea, said the offer to its 450,000 health members contained some concessions from the government, such as a pledge that staff less than 10 years from retirement will keep their existing pension arrangements, while those earning under £26,000 will escape a contributions increase next year.

McAnea said: "On some issues – such as contribution rates for the low paid next year, and for people close to retirement – we have made progress. On others, we always knew this would be a damage limitation exercise aimed at reducing the worst impacts of the government's pension changes."

Responding to the progress in talks on the NHS pension scheme, Dean Royles, director of the NHS Employers organisation, said: "This significant step forward will help lift the cloud of uncertainty hanging over the NHS around pensions and industrial action. This period of uncertainty has led to anxiety for NHS staff. Disruption to NHS services through industrial action and has meant distress for patients."

Union activists have scheduled a meeting for 7 January at which further strike action could be on the agenda, with the PCS in a position to cause some disruption through its membership among UK Border Agency employees.

However, airports and ports escaped serious disruption during the 30 November walkouts, in which the PCS took part.

The government is seeking major changes to the schemes: contribution increases averaging 3.2 percentage points by 2014-15; pegging the pension age for public sector employees to the state pension age and switching people in final salary schemes to career average schemes.

In a joint statement, local government unions stressed that they were signing off on a negotiation framework and not a final deal, which would have to be voted on by members.

"We believe that – if agreed – the principles under discussion will provide a very positive framework for negotiations and potentially could lead to no change until 2014," they said.

Barber said: "We have been talking for many months but since the day of action that involved millions, and with the intensive discussions over recent days, we now see change. Accrual rates are more favourable than were originally proposed, there is enhanced protection for those nearing retirement, Fair Deal protection for those whose jobs transfer out of the public sector, and there will be no adverse changes to pensions for 25 years."