After the Tories suffered heavy losses to the UK Independence Party in the council elections, Mrs May said it was essential voters believed the party would honour its promise to hold an in/out referendum on EU membership after the next general election.
However she rejected calls from some senior Conservatives to bring forward the date of the referendum and stage it in this parliament in order to finally kill off the appeal of Ukip to Tory voters.
She said that it was important that they stood by David Cameron's plan to re-negotiate the terms of Britain's membership and then put the new settlement to the country.
"If you want to take a re-negotiated settlement to the British people, you have got to re-negotiate it," she told the BBC Radio 4 Today.
More top news
Three men accused of mixing beef with horsemeat and passing it off as beef are being charged with fraud, the CPS have announced.
Several coastal towns in the south east and north of the country, including Nice and Le Touquet, had banned the body-covering swimwear.
Karen Jones put out a plea for people to help after she found her autistic son Ollie making birthday cards to open on his 15th birthday.