Theresa May needs the votes of the DUP's 10 MPs to prop up her minority administration as she hopes to steer government business - including crucial measures on Brexit - through the Commons.
The government's plan for the next parliament will be outlined in the Queen's speech on Wednesday, and will include laws needed to deliver Brexit and new immigration legislation.
Guy Verhofstadt, the European Parliament's Brexit coordinator, said that Brexit can be halted, but if Britain reversed course it should not expect to keep getting its EU budget rebates or opt-outs from key EU rules.
Liberal Democrat MP Alistair Carmichael said: The Conservatives can not go from weak and wobbly to business as usual in three days.
Like many in the bloc, Mr Verhofstadt has always been critical of the rebate that then-prime minister Margaret Thatcher secured in the 1980s, which means Britain gets about half of its European Union budget contributions back.
The Prime Minister is to hold talks with political leaders from Northern Ireland in a bid to allay fears the anticipated parliamentary deal with the Democratic Unionists will undermine the peace process.
"Following discussions in Brussels today, both sides agreed that the formal negotiations under the Article 50 process can now start", the statement said.
Brexit talks in Brussels on Monday will focus on the status of expats, the UK's "divorce bill" and the Northern Ireland border, rather than on future trade relations with the European Union, it has been confirmed.
With the two-year clock on Brexit ticking since March, when a letter from May formally started proceedings, Barnier dismissed the suggestion of postponing the negotiations and said such a delay would only prompt further instability.
May wants to negotiate the divorce and the future trading relationship with the European Union before Britain leaves in March 2019, followed by what she calls a phased implementation process to give business time to prepare for the impact of the divorce.