"We are continuing to have talks but today, as you will imagine, there has been a real focus on this bad tragedy in London", May said.
The Brexit negotiator asked London not to "waste time" and explained that it will take "several months to draw out the conditions of an orderly withdrawal, with hard and sensitive points of discussion".
Theresa May travelled to Paris this evening to meet with French president Emmanuel Macron.
Parliament now "deserves a say", he said, adding that there was "perhaps an opportunity to consult more widely with the other parties on how best we can achieve it".
The British general election last week has done little to remove the uncertainty facing the business community and Britain's worldwide partners as it delivered a shock hung Parliament, forcing the government to turn to the right-wing Northern Irish Democratic Unionist Party (DUP) for support.
The talks are being closely watched in European capitals as they could delay the expected start of Brexit negotiations next week, as well as change Britain's entire approach to its EU withdrawal.
"We stand at a critical time with those Brexit negotiations starting only next week - I think that stability is important".
Guy Verhofstadt, the European Parliament's chief Brexit negotiator, warned the United Kingdom risks a "brutal exit" if discussions aren't concluded within two years.
"It's passing quicker than anyone believes. We are ready as soon as the United Kingdom itself is ready", he said.
France's Macron said the door was still open for Britain to remain in the European Union, though he added that it would be hard to walk back once negotiations start. This is all the more so, given the alliance with the DUP, for whom an open border with the Republic of Ireland is a priority.
They would not form a coalition.
But Sir John said he was "concerned" about the impact any agreement between the DUP and the Conservatives might have on Northern Ireland's peace process, warning it could mean the Government would no longer be regarded as impartial.
London's neutrality is key to the delicate balance of power in Northern Ireland, which was once plagued by violence over Britain's control of the province.
Arlene Foster, the DUP leader, whose 10 MPs representing Northern Irish seats in Westminster hold the fate of May's government in their hands, said Tuesday that discussions on a deal to support the Conservatives in parliament were "going well".
Theresa May insisted the Government was "absolutely steadfast" in its commitment to the Northern Irish peace process as she faced questions on whether a DUP-Tory alliance would put fragile agreements at risk.
Liberal Democrat leader Tim Farron called for a cross-party committee to be set up to handle the Brexit negotiations.
Baker has been instrumental in organizing backbench support for May's Brexit strategy, and, before the referendum famously described government efforts to sell David Cameron's European Union renegotiation to Tory backbenchers as "polishing a poo".