Theresa May is set to meet the leader of the Democratic Unionist Party in Downing Street as she seeks a deal to enable the Conservatives to govern.
The prime minister will host Arlene Foster to thrash out the terms of the DUP’s backing for her minority government.
Mrs May says they will have no veto on key policies. Ms Foster says her party has the national interest at heart.
MPs are returning to Westminster on Tuesday following the election.
The Commons will choose a new speaker and Lords will begin to be sworn in during the afternoon.
Later, the Prime Minister will hold talks with French President Emmanuel Macron, including looking at how to tackle online radicalisation and terrorism.
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The Conservatives are having to rely on the support of 10 DUP MPs after they fell eight seats short of winning an overall majority at the general election.
Mrs May apologised to Tory MPs on Monday, accepting personal responsibility for failing to win an outright victory and sacrificing the parliamentary majority she inherited from David Cameron when she became leader last year.
She told a meeting of backbenchers that she had got the party into “this mess” by calling the snap election and now “I’ll get us out of it”.
Her performance was roundly praised by Conservative MPs, some of whom were openly questioning her future over the weekend.
In an article for the Telegraph on Tuesday, the new environment secretary Michael Gove – who has clashed with Mrs May in the past – said she was the ideal person to secure a Brexit agreement that “commanded the widest possible support” given her track record of “seeing through vital jobs to the end”.
Amid calls from some MPs for the Conservatives to rethink their Brexit strategy, he said there was a “clear consensus” for leaving the single market and ending free movement while retaining the “maximum access” to EU markets and maintaining co-operation in key areas such as science.
But in an article for the Financial Times, the EU’s chief negotiator Michel Barnier has warned the UK that there is “no time to waste” to get the process – which has 18 months to run – under way. Mrs May will herself meet French president Emmanuel Macron on Tuesday for talks.
Conservative chief whip Gavin Williamson flew to Belfast on Saturday to begin formal discussions with the DUP after the election resulted in a hung parliament. The expectation is that details of a so-called “confidence and supply arrangement” in which the DUP will guarantee their backing for the Queen’s Speech and future government Budgets will be agreed in the coming days.
The agreement is expected to be very different in nature to the coalition deal agreed between the Conservatives and Lib Dems in 2010, with DUP politicians not getting cabinet jobs and their support for other legislation to be determined on a vote-by-vote basis.
Tuesday’s discussions are likely to focus on the government’s legislative plans for the year ahead as well as the upcoming Brexit negotiations, due to begin next week, and their particular implications for Northern Ireland’s border with the Republic of Ireland and trade.
There has been uncertainty as to whether any deal will be agreed in time to allow the Queen’s Speech to take place as planned on 19 June.
It is expected that Conservative manifesto commitments that might have proved problematic for the DUP – such as cuts to winter fuel payments and the removal of the triple lock guarantee for pensioners – will be watered down or ditched altogether.
Some MPs have expressed disquiet at the Conservatives tying their fortunes to a party which is opposed to equal marriage and has expressed its support for tightening the laws on abortion – but No 10 has insisted these issues will not be up for grabs in any way.
Speaking on Monday, Ms Foster rejected suggestions that the mooted deal could undermine a return to power-sharing arrangements at Stormont, amid claims from political rivals that the government’s stated impartiality would be fatally undermined.
She said a deal between the Democratic Unionist Party and the Conservatives – who have informally been building links for some time – could be a “tremendous opportunity” for Northern Ireland.
“We are going into these talks with the national interest at heart,” she said.
“The Union, as I said before, is our guiding star. We believe in the Union, we believe in national stable government and that will be at the forefront of our mind going into these talks again tomorrow.”
Sinn Fein President Gerry Adams has warned that no arrangement between the Conservatives and the DUP would be good for Northern Ireland but Northern Ireland Secretary James Brokenshire has said the negotiations are “entirely separate from our intent and desire to see devolution restored here”.