May's Conservative Party needs the support of the DUP's 10 MPs in order to retain power in the House of Commons, after losing her majority in last weeks "snap" United Kingdom election.
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.
An organiser for the Women's March said the event was "for self-defining women, kids, non-binary people and all who love and support us".
The Democratic Unionist Party controls the Northern Irish Assembly.
"Yesterday Emmanuel Macron, the new French president, spoke about an open door, he said if Britain is changing its mind it will find an open door", Verhofstadt told the European Parliament.
Both the Conservative Party and the DUP were now focused on finalising the "terms and conditions" of the deal following a meeting between May and DUP leader Arlene Foster on Tuesday, the DUP source told the channel.
The move comes amid concerns the Government will compromise its stated impartiality in the region if it enters a confidence and supply deal with the DUP at Westminster.
Sinn Fein, which won seven seats in the British parliament last week but does not take up its seats or vote in Westminster, would likely reject a deal to form a government by refusing to work with the DUP in Northern Ireland.
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Last evening, May faced the tough 1922 Committee of her party's backbench MPs amid a brewing rebellion within the ranks after her gamble to call a snap general election backfired, leaving the Tories eight seats short of a majority.
May will also be reliant upon the 10 lawmakers from the eurosceptic DUP, who would help her edge past the 326 votes needed in parliament to avoid the government collapsing.
The European Parliament, which named former Belgian prime minister Verhofstadt as its Brexit pointman previous year, will have the final say on any deal on Britain's exit from the EU.
"Obviously it's not great that things are being delayed", an European Union source said on condition of anonymity, adding that Brussels officials had been "glued to their TV screens and Twitter" for the British election results.
Under the deal, the party would offer support for key votes, such as backing the Queen's Speech and the Budget, and - crucially - in any votes of no confidence.
The so-called "soft border" issue is also one of the top agenda items for Brussels in the upcoming Brexit negotiations.
Senior British minister and prominent Brexit campaigner Michael Gove said on Tuesday that Britain will leave the EU customs union, which guarantees tariff- free trade within the bloc but prohibits members from striking third-party trade deals.
Sir John who was instrumental to end the IRA conflict in Northern Ireland spoke to BBC Radio 4's World at one programme and warned that about "hard men, lurking in the corners of the communities" saying that "that they wish to return to some sort of violence".
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