The British and Irish prime ministers are holding a series of meetings with the Northern Ireland parties.
After meeting Sinn Féin and the DUP, Theresa May and Leo Varadkar were due to meet the Alliance Party, the SDLP and the UUP.
It comes amid speculation the DUP and Sinn Féin are close to agreeing a deal to restore devolved government.
Earlier, the prime minister and taoiseach (Irish Prime Minister) met to discuss restoring Stormont and Brexit.
- Stormont deadlock: Need-to-know guide
- Tory-DUP deal: What you need to know
- Profile: Sinn Féin’s new leader Mary Lou McDonald
Speaking after meeting the prime minister, DUP leader Arlene Foster said: “There isn’t a deal yet, what there is, is very good progress.”
She said her party wanted a deal that was “sustainable into the future”.
Sinn Féin President Mary Lou McDonald said the talks had reached “a decisive phase”.
“What is required now is the political will to make it happen,” she said.
Prior to arriving at Stormont, Mrs May visited Bombardier’s plant in Belfast.
She met factory floor workers and was shown the capabilities of the multi-million pound plant which is the main production site for wings for the C-Series.
Her visit came just over two weeks after Bombardier’s victory in a trade dispute with rival aerospace firm Boeing.
The US International Trade Commission (ITC) overturned a decision to impose damaging tariffs on US imports of its C-Series aircraft, which would have placed jobs in the Belfast factory at risk.
Several previous rounds of talks between the DUP and Sinn Féin have, so far, failed to break the political deadlock.
A DUP source told the BBC a deal “is not likely” on Monday.
Northern Ireland has been run by civil servants since the power-sharing executive made up of the DUP and Sinn Féin collapsed in January last year.
The then deputy first minister, Martin McGuinness, pulled Sinn Féin out of the coalition after a series of disagreements with the final straw being the DUP’s handling of a scandal over green energy scheme.
Mrs May last visited Northern Ireland in May when she toured the Balmoral Show ahead of a snap general election.
Since then, she has struck a parliamentary deal with the DUP and has faced criticism for adopting a hands-off approach to the deadlock at Stormont.
Among the issues that have divided the parties is Sinn Féin’s demand for an Irish language act.
By BBC News NI political correspondent Mark Devenport
The Irish language act has been a major stumbling block, with DUP leader Arlene Foster promising previously that it wouldn’t happen on her watch.
What I am led to believe is that there could possibly be a very strange, legislative fudge which would see the creation of three separate bills, one for the Irish language, one dealing with Ulster Scots and one for wider cultural issues.
The suggestion is that these three bills would end up merging together as one act in an attempt to spare blushes on all sides.
On marriage equality, I am not exactly sure how they are going to sort that one out, but one option that has been discussed is the possibility of bringing a private member’s bill on the issue or deferring responsibility to Westminster.
At least three or four DUP MLAs would be pretty hostile to the notion, but equally there are some who would support it, or at least not object
A Downing Street spokesman said the prime minister would remind the parties of the many pressing issues facing Northern Ireland and make clear her belief that a fully functioning executive is the best way to serve the interests of the whole community.
A spokesman for Leo Varadkar said the taoiseach would use his visit to “assess the state of play” and “encourage the parties to reach an agreement”.
“The (Irish) government has consistently said that the restoration of the institutions is essential in the context of full implementation of the Good Friday Agreement, and that it will continue to work very closely with the British government to support the northern parties to achieve this outcome,” he said.
At the weekend, Sinn Féin’s vice president Michelle O’Neill predicted that the Stormont talks would conclude this week.
Her comment strengthened speculation that a compromise between her party and the DUP could soon be unveiled.
Theresa May and Leo Varadkar meet Stormont parties}