Fears have been raised that Westminster would damage its role as impartial mediator in the peace process.
The 1998 peace accord, which provides the template for powersharing at Stormont, commits the United Kingdom and Irish governments to demonstrate "rigorous impartiality" when it comes to the differing political traditions in Northern Ireland.
"To use that as a means of trying to disrupt the government's policy on unrelated matters..."
After the meeting with Mrs Foster the Prime Minister left Number 10 and Labour leader Jeremy Corbyn congratulated Mrs May on "returning as PM" and said he "looked forward to this Parliament, however short it may be". The Prime Minister reiterated that the Government's approach and objectives in the forthcoming talks to re-establish the Northern Ireland Executive remained unchanged.
May announced last Friday following her humiliating defeat in the general election that she would be allying with the pro-Brexit DUP party to gain a 13-seat Conservative majority.More news: Dennis Rodman, diplomat? He's back in North Korea
Northern Ireland's political parties are set to meet with Mr Brokenshire and Irish Minister for Foreign Affairs and Trade Charlie Flanagan at Stormont today.
The DUP replaced the SDLP in South Belfast, wrested back South Antrim from the UUP and saw off the challenge of the Alliance Party and Sinn Fein in East and North Belfast respectively. All those involved must engage in the full knowledge that the deadline of 29 June is final and immovable.
"Equally the Government is taking a risk by coming into a close relationship with them for obvious reasons". "I am dubious about it", Major told BBC radio.
One of the most pressing issues is the state of the border between Northern Ireland and the Republic of Ireland after Britain leaves the EU.
She warned that a outcome of failing to re-establish a power-sharing executive would be the return of direct rule, with decisions on devolved issues being taken by the London government.
Commenting on whether the talks might result in the restoring of power sharing institutions due to the threat of the alternative of direct power controlled from Westminster by a Government involved with the DUP, he said: "Well that might be a positive outcome, I think we should be grown up about this". "Their choice in the next three weeks will shape Northern Ireland's future".