With Home Secretary Amber Rudd, Brexit Secretary David Davis, and Defence Secretary Sir Michael Fallon all retaining their posts, there was speculation any reshuffle could be limited to replacing the eight ministers who lost their seats in the election.
"This is a serious moment for the United Kingdom economy", said Carolyn Fairbairn, the head of Britain's biggest business lobby, the CBI.
A senior Conservative lawmaker was in Belfast on Saturday for talks with the DUP, a spokeswoman for May's office said.
He said: "I worked very well with Theresa May and I think she has intelligence and integrity".
May called the snap election saying that she needed a strong majority to put her in a powerful position over negotiating Britain's departure from the European Union, a process that is due to begin on 19 June.
"The renewable and clean tech industry has been waiting for almost a year for the release of the Clean Growth Plan and it's now critical for us that we have a clear commitment and direction, no matter what shade of Government".
Deputy Leader of the Northern Irish Green Party Clare Bailey echoed those concerns, telling BuzzFeed News: "The resolution of legacy issues should not be compromised by any arrangement between the DUP and Conservatives". I have said that was a problem.
She said any changes to her personal team would be for another day after colleagues criticised the way May ran the campaign. And they also harnessed social media.
"She might still be Prime Minister, but May has to pass a Queen's speech in a week's time - this will be hugely hard, as there are many aspects of the Conservative manifesto that not every MP supported".