Speaking earlier on Tuesday, DUP leader Arlene Foster told reporters that discussions centered on "bringing stability to the United Kingdom government in and around issues around Brexit, obviously around counter-terrorism, and then doing what's right for Northern Ireland in respect of economic matters".
A June 29 deadline has been set for the establishment of devolved power sharing government in Belfast.
"We continue to work with all the parties in Northern Ireland and the Republic of Ireland in ensuring that we can continue to put in place those measures necessary to fulfil those agreements, " she said.
"Ultimately, I think the parties understand people voted in the March Assembly elections for a strong voice at Stormont".
He said: "We will continue to take the fight to the Tories and I will be out campaigning around the country in Conservative marginals in those extra seats we need to gain to deliver the government for the many that nearly 13 million people voted for last week".
With her tally of Conservative MPs slashed to 317 in last week's poll, Mrs May needs the backing of the DUP's 10 members to reach the 320 required for a working majority in the Commons.
The proposed "supply and confidence" deal would see the DUP back the Conservatives in votes on the Budget and confidence motions.
58 missing, presumed dead in London fire : London police
Two Underground lines near the fire area were partially shut down on Saturday to make sure that debris did not land on the tracks. Firefighters are still searching for victims in the 24-story Grenfell Tower that went up in flames early Wednesday.
If the announcement of the deal is delayed, then the Queen's speech, which is supposed to happen on Monday, June 19, could also be delayed by at least a week. O'Neill said she will also travel to Dublin in the coming days to meet with new Irish Prime Minister Leo Varadkar.
"It's going to be hard".
"I think there will be pressure for a softer Brexit", Mr Cameron added, saying that Parliament now "deserves a say" on the issue.
That would help safeguard jobs and trade with European Union members but would severely restrict the UK's ability to strike its own trade deals around the world.
"There is a unity of goal among people in the United Kingdom", May said following a meeting with French President Emmanuel Macron in Paris.
"Until the negotiations come to an end, of course there is always the possibility to re-open the door", said the French President.
"It's a unity of goal, having voted to leave the European Union, that their Government gets on with that and makes a success of it, and we are committed to developing a deep and special partnership with the EU".
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