Chancellor Philip Hammond has hinted he would like to drop the party's 2015 manifesto pledge not to put up income tax, VAT or national insurance contributions (NICs) during the lifetime of the parliament.
Attending the spring meeting of the IMF in Washington, Mr Hammond - who was forced into a Budget U-turn after critics said his changes to NICs for the self-employed breached that commitment - said he needed more "flexibility" in managing the economy.
His comments were seized on by Labour, which accused the Tories of planning "a tax bombshell" while the Liberal Democrats suggested they would hit "white van man".
However, the Financial Times reported that aides to the Chancellor in Washington were insisting no decision had been taken on whether to drop the tax pledge from the Conservative manifesto for June's election.
The row came after Mrs May risked angering traditionalist Conservatives after she reaffirmed the Government's commitment to international aid spending while refusing to guarantee the "triple lock" for pensioners.
Her announcement, during a campaign visit to her Maidenhead constituency on Friday, that she would stick by David Cameron's commitment to spend 0.7 per cent of GDP on international aid, was sharply criticised by some Tories.
Former party chairman Lord Tebbit told The Daily Telegraph: "It is a very bad start to the campaign to insist on increasing aid every year whilst there is not sufficient money for the NHS. It does not seem to make good politics to me."
Sir Gerald Howarth, a Conservative former defence minister who is standing down at the election, told the paper: "It is so immoral to be spending £13 billion on overseas aid.
"It is taxpayers' money when social care is under pressure, NHS is under pressure, schools are under pressure."