On Brexit, the DUP leader said she believes high tech equipment to monitor goods crossing the Irish border will be ready in time for the UK's departure from the EU.
Mrs May is on-the-clock to sign off on the Queen's Speech, due to be unveiled in parliament next Wednesday.
Arlene Foster's leadership of the Democratic Unionists remains a stumbling block that could scupper crunch talks to end a powersharing stalemate in Northern Ireland, Sinn Fein has warned.
There are questions over how long Foster, who was the minister with responsibility for the scheme from its inception in 2012 until 2015 - knew the initiative was flawed. "We are leaving the European Union, but we are not leaving Europe, and we want to remain committed partners and allies of Ireland and all our friends across the continent", said May.
The Conservatives have been in negotiations with the DUP since Mrs May lost her Commons majority in the General Election earlier this month. Failing that it must consider the introduction of direct rule from Westminster, or the more unlikely option of new Assembly elections for the North.
The DUP has said it will act as a "brace against hard austerity" in its deal with the Conservatives and Labour could put down amendments to torpedo various austerity measures, including the bedroom tax, school cuts and means-testing winter fuel payments for pensioners.
Australia suspends air combat missions over Syria
Coalition aircraft conducted a show of force and stopped the initial pro-regime advance toward the town, the Pentagon said. The drone shot down on June 20 was "just outside" the deconfliction zone, according to USA officials who spoke to CNN .
Sinn Fein is not budging on its insistence that Arlene Foster can not return as Stormont first minister while a public inquiry into a botched green energy scheme is ongoing, Gerry Kelly has made clear.
She had been asked whether May was confident she was still the right person to lead the country.
The former Northern Ireland First Minister said her meeting with Mr Varadkar was very good and that she was looking forward to a very positive relationship with the Irish premier.
Mr Adams said he was pushing the Taoiseach to raise the prospects with London of a border poll within five years on the future of the North and prospective Irish re-unification.
On Brexit, Ms Foster said her party wanted to see "a sensible Brexit and one that works for everybody".
Shadow Brexit secretary Sir Keir Starmer said the talks had begun badly because Mrs May lacked authority and a mandate.
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