Penny Mordaunt has refused to explicitly back Theresa May’s Chequers plan for Brexit, increasing pressure on the government not to make dramatic concessions to Brussels in the crucial days ahead.

The international development secretary said she would not give a “running commentary” on the proposals when asked if she supported them, saying simply that the ball was “firmly” in the EU’s court on what happened next.

However, while Mordaunt insisted the prime minister had her support for now, the pro-Brexit minister raised the possibility that this could be conditional if the final deal looked like an “attempt to derail or fudge” the outcome of the Brexit vote.

“The prime minister can count on my support. But what I would say is that we don’t know where this is going to end up. We are at a critical moment now. The ball is firmly back in the EU’s court; we are waiting for them to respond,” she said.

In her remarks to an audience of development officials and journalists, Mordaunt also set out plans to privatise a proportion of the £14bn aid budget, effectively cutting the amount of public money that goes into meeting the 0.7% of GDP commitment.

Mordaunt is one of two leave-voting cabinet ministers who have not yet delivered a public verdict on May’s Chequers plans. Her remarks, which will fuel leadership speculation, came as the Brexit secretary, Dominic Raab, prepared to face down mutinous Eurosceptic Conservative MPs in the House of Commons.

The former Brexit minister Steve Baker, the vice-chairman of the European Research Group of Brexit-backing MPs, said he believed at least 40 MPs were prepared to vote against the government if the EU agreed a Chequers-style deal.

However, cabinet ministers have told the Guardian they expect between 10 and 20 Brexiter rebels. May has also drawn up plans for a secret charm offensive aimed at persuading dozens of Labour MPs to back her Brexit agreement, the final elements of which are being thrashed out in Brussels.

Mordaunt said: “I think we need to let the prime minister and her negotiating team get on with it and I’m supporting her in doing that, I think that’s in the national interest. So I’m not going to give a running commentary on that.”

In a pointed remark directed at the former foreign secretary Boris Johnson, a potential leadership rival, and the former Brexit secretary David Davis, she said: “Other members of the cabinet felt that it was not the best way that they could support, but it was certainly my view that is the best way I can support.

“All that matters is where we end up, what that agreement is, and I’m going to do everything I can to ensure that is the best deal possible. I feel very strongly that we must honour the result of the referendum and the expectations of the British public in that.

“I think [May] is working absolutely flat out to get our country the best deal possible. I don’t doubt her motives, I don’t doubt her commitment and I don’t doubt for one moment her understanding that we have to deliver a good Brexit; we have to honour that result. So she has my support and I am not in any way expecting that situation to change.”

In her speech, Mordaunt announced she wanted to rewrite international rules to allow profits from development projects to be included in the UK’s 0.7% GDP spending commitment, cutting the sums required from the taxpayer by hundreds of millions of pounds.

In a signal to Tory aid sceptics that she is committed to providing value for money, she said private cash already invested in the poorest countries via her department’s development vehicle, CDC, was “doing good, while making money”.

“We want to use our aid to mobilise the private investment needed to fill the financing gap needed to deliver the global goals, tackling the barriers that prevent more investment flowing into developing countries.”

Mordaunt also said she wanted a national conversation around aid spending, with the public given the chance to invest savings and pensions in schemes that supported development.

“We want to give British savers the choice to make a financial return in exchange for their goodwill to change the world for the better.” she said.

The shadow international development secretary, Kate Osamor, said the proposal to change the rules on what could be included in the 0.7% was a “outrageous distortion” of Britain’s overseas development programme.

“The Tories’ plans to rewrite the international rules on aid and slash billions of pounds of public money will do nothing to end global poverty or reduce inequality,” she said. “Poverty is not a commodity.”