Mr Eastwood said in a statement: "The context in which the talks process is now being asked to operate in could have very serious consequences if there is any suggestion of a back room deal with the DUP".
An initial round of talks between May and DUP leader Arlene Foster ended with no agreement on Tuesday, although both sides said they were hopeful of a deal.
The proposed deal would see the DUP back the Conservatives in votes on the Budget and confidence motions.
The Prime Minister did not mention the ongoing deliberations as she addressed MPs but called on Parliament to "come together in a spirit of national unity" to deal with the challenges facing the country.
"It's going to be hard, there's no doubt about that, but perhaps an opportunity to consult more widely with the other parties on how best we can achieve it", he said at a conference in Poland, the Financial Times reported.
As European leaders tried to fathom exactly how Britain would begin the negotiations, German Finance Minister Wolfgang Schaeuble said Germany wanted a Brexit deal that would limit negative consequences for the bloc but also did not want it to weaken Britain. "It will be a brand new door, with a new Europe, a Europe without rebates, without complexity, with real powers and with unity", Verhofstadt said. "Scotland voted against Brexit".
The Government has actually acted in good faith and I think again this is just being, trying, looking for something with which to attack the Government and what they should do is to concentrate on the realities of the situation.
"I can't negotiate with myself", Mr Barnier, the EU's Brexit negotiator, told European newspapers including The Financial Times.
"The only thing I know is that there is an Article 50 request and we have been preparing ourselves for a long time to start negotiations on that basis".More news: Sanders condemns shooter who 'apparently' volunteered on campaign
Mrs May stressed that Brexit would happen and the timetable remains on course.
Mrs May headed to Paris later Tuesday to meet with French President Emmanuel Macron, and the two leaders attended a friendly football match between France and England. "It's a unity of objective, having voted to leave the European Union, that their government gets on with that and makes a success of it".
He told the MPs and peers: "We must remain in permanent campaign mode on a general election footing".
Theresa May insisted the Government was "absolutely steadfast" in its commitment to the Northern Irish peace process as she faced questions on whether a DUP-Tory alliance would put fragile agreements at risk.
The move comes amid concerns the British government will compromise its stated impartiality in the region if it enters a confidence and supply deal with the DUP at Westminster.
Major said "a fundamental part of that peace process is that the United Kingdom government needs to be impartial between all the competing interests in Northern Ireland".
"It just illustrates the chaos that the Conservative Party are in at the moment".
"Going overseas and being seen to be the prime minister and talking to the president of France, being seen to be wheeler-dealing on the worldwide stage, is a classic move to shore up authority at home", he told AFP.
She said: "We accept the fact that, if we are going to have impediment-free access to the single market, then there will have to be some element of free movement".
But with so much at stake for Britain and its US$2.5 trillion (S$3.5 trillion) economy, pressure was mounting on May from within and without her party to heed other voices.