Tories have made clear since last week's election that their discussions with the DUP revolve around assurances of support in key Commons votes, rather than a full coalition.
She met DUP leader Arlene Foster, whose Eurosceptic Northern Irish party has 10 parliamentary seats, for more than one hour of talks in Downing Street.
Former Tory Prime Minister John Major, who has raised concerns about the potential alliance, warned the more extreme elements in both Catholic and Protestant communities could see an opportunity to re-enter the fray.
Mrs May added: "My government remains absolutely committed to doing everything we can to help take this process to a successful conclusion, remaining steadfast to our commitments in the Belfast Agreement and its successors".
"Although I don't expect it to suddenly collapse because there's a broad consensus that wishes it to continue, I think we have to take care with it".
May held talks with the Democratic Unionist Party (DUP) on Tuesday in a bid to avoid another election.
"The intent is to ensure that we have the stability of Government in the national interest".
Mr Brokenshire, who will also attend the Downing Street exchanges, characterised the meetings as a contribution to the three-week process to restore devolution.
He said that he believed that if a deal is reached, the government "will not be seen to be impartial" which will create problems for communities in the North.More news: Pakistan's Mohammad Amir fit and plays in Champions Trophy final
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The DUP leader said: "There's been a lot of commentary around the issues that we are talking about and it won't surprise anyone that we are talking about matters that pertain, of course, to the nation generally".
Manfred Weber, the German head of the centre-right European People's Party, the largest group in the assembly, said May now has "no majority" for a so-called hard Brexit, in which Britain leaves the EU with no deal on the divorce terms or on future relations with the EU.
"It is clear that our country faces some of the greatest challenges of our time", she told parliament.
Jeremy Corbyn, leader of the opposition Labour Party, which saw its number seats and share of the vote increase, said there could be another election this year or early in 2018 after last Thursday's vote produced no clear victor.
Jeremy Corbyn, leader of Britain's main opposition, said his Labour Party would not support the Queen's speech to try to force her out of power through a vote of no-confidence. "The current uncertainty can not continue", he said on Twitter.
"She said "I'm the person who got us into this mess and I'm the one who is going to get us out of it", said one Conservative lawmaker who attended the meeting.
Mrs May had also said no deal would be better than a bad deal, when planning to carve out a hard Brexit. As my colleague Adam Bienkov reported on Monday, May is set to shelve contentious proposals like the plan to lift the ban on new grammar schools and the social care policy that played a big role in costing the party its majority.
There is frustration among European Union leaders and officials that three months have already passed since May triggered Article 50, the device which started the Brexit process.