Theresa May will go to Paris and Berlin to plead with Angela Merkel and Emmanuel Macron for a Brexit extension on Tuesday, promising to be a good member of the European Union until departure day and claiming talks with Labour have a serious chance of reaching a deal.

Before an emergency European summit this week, the prime minister will head to the continent to make the case for extending article 50 only until the end of June. However, she is also being forced to make pledges that the UK would abide by EU rules for however long it is a member, given that a longer delay and participation in European elections now look like the most likely option.

EU leaders will decide at the talks on Wednesday night whether to grant an extension to article 50 at all but are most likely to offer a longer delay of up to a year involving strict conditions forcing the UK into “sincere cooperation” with the rest of the bloc.

That prospect appeared to be acknowledged on Monday when the Conservative party drew the ire of hard Brexiters – already seeking an indicative confidence vote in the prime minister – by telling potential local election candidates it is preparing to fight in the European elections in May, and asking potential MEPs to put themselves forward.

To avoid EU elections, May would probably have to pass her deal by 12 April and have all the necessary legislation pushed through parliament by the day of the polls on 23 May. If no extension is granted and no withdrawal agreement passed, the UK will leave the EU without a deal on Friday.

With a year-long delay now on the cards, May embarked on a frenzy of last-minute diplomacy on Monday to reassure leaders that the UK would not seek to cause trouble during that period, even though one foot would be out of the door. This would mean a pledge to refrain from holding up processes such as the budget setting and potentially even step back from big decisions that relate to future issues after Brexit.

After speaking to May, Mark Rutte, the Dutch prime minister, said: “Crucial to know when and on what basis UK will ratify the withdrawal agreement. A positive decision hinges also on assurances from UK on sincere cooperation.”

His position reflected alarm among European leaders about threats from Eurosceptics to cause problems in Brussels if the UK’s membership is extended, especially if there were to be a new prime minister in favour of a hard Brexit. Jacob Rees-Mogg, the Tory MP who leads the European Research Group, has argued that the UK should “use the remaining powers we have to be difficult” in the event of long delay and claiming that “sincere co-operation so far seems to be a one-way street”.

The prime minister will argue in public that there is no need for a longer extension, as talks with Labour are continuing and due to resume at ministerial level on Tuesday. However, neither side privately believe there will be a deal signed this week.

The Labour leader, Jeremy Corbyn, revealed that the government had not yet made any offer to sign up to a customs union, making it difficult to see how a deal could be done before the EU summit.

“The government doesn’t seem to be moving off its original red lines,” he said, before further technical talks between officials on Monday evening.

But in a meeting with Ireland’s taoiseach, Leo Varadkar, in Dublin, the EU’s chief negotiator, Michel Barnier, signalled that the EU was for its part “happy” to negotiate a customs union. Keir Starmer, the shadow Brexit secretary, also said the government was still trying to persuade Labour that a customs union was really contained in May’s deal “if only we looked a bit harder”.

Downing Street is understood to have made an offer to enshrine guarantees on workers’ rights and environmental protections into UK law, making it more difficult for a new prime minister to undo them. But the proposals do not approach Labour’s key demand for a permanent customs union.

Sources close to the talks said senior cabinet ministers were divided on whether to make a bolder proposal to Labour to achieve a deal in time, involving some kind of customs arrangement, with some government figures such as David Lidington pushing for more concessions than May is currently willing to offer. However, a Cabinet Office source disputed that characterisation, saying Lidington and others were still in “listening mode” at this stage.

Pro-Brexit Conservative MPs are furious with May over both the prospect of a deal with Corbyn or the alternative of a long delay to Brexit if no agreement is reached. There is still the possibility of cabinet resignations if May is forced down either route.

Backbenchers are plotting fresh attempts to oust May by trying to prove she has lost the support of a majority of her MPs, with the 1922 Committee of backbenchers split on whether to allow an indicative ballot on her leadership.

With Conservative backbenchers already in open revolt, a move towards a deal involving a customs union with Labour support would be politically explosive for May. Boris Johnson, who is one of the favourites to succeed May, has said that “surrender” on a customs union is something that “cannot, must not and will not happen”.

However, the idea of a long delay to Brexit is equally problematic for May, as pro-Brexit cabinet ministers such as Andrea Leadsom and Penny Mordaunt have said they cannot support that or participation in the EU elections.

Asked about why May was dashing to Berlin and Paris before the EU summit, her official spokeswoman said: “This is obviously a unique European council specifically focused on Brexit. The PM set out a clear ask in terms of an extension and it is important that she set out the rationale for that.”

Macron, the French president, has been a leading voice among EU leaders demanding that May sets out a clear purpose for an extension, which could be a general election or second referendum. However, other EU leaders have taken a softer line on granting an extension and the final decision is likely to be taken at a “pre-meeting” of six of the most powerful leaders before the summit.

It is still not clear what the extension would be used for, if May fails to find a consensus with Labour or persuade more backbenchers to support her deal, but Conservative MPs would be likely to push for a change of leadership.

May has already asked for an extension to article 50, but a cross-party bill making her legally bound to seek a delay to prevent a no-deal Brexit cleared parliament on Monday. The government has now tabled an amendable motion for debate on Tuesday saying it will seek a delay to Brexit until 30 June.