Britain's Prime Minister Theresa May leaves 10 Downing Street for her weekly Prime Minister's Questions in the House of Commons in London. File photo: AP Photo/Alastair Grant.

London - British Prime Minister Theresa May says she will make a "new, bold offer" to lawmakers in the coming weeks, when she will try once again to win a majority in parliament for her Brexit deal.

Writing in the Sunday Times newspaper, the Conservative prime minister expressed optimism that members of parliament will back her deal to leave the European Union at the fourth time of asking.

"I still believe there is a majority in parliament to be won for leaving with a deal," she wrote.

The bill "will represent a new, bold offer to MPs across the House of Commons, with an improved package of measures that I believe can win new support," May wrote, promising the deal will honour the decision the British people took in the 2016 referendum to leave the EU.

May has so far failed to resolve the parliamentary impasse over Brexit, forcing her to extend Britain's scheduled leaving date by seven months until October 31. The delay also meant Britain will take part in next week's European Parliament elections.

In the op-ed, she urged voters to choose her party next week, claiming that Labour and other opposition parties "cannot deliver Brexit or have so far refused to do so."

She also appeared to blame "some MPs on my own side" for failing to pass a deal so far, in an echo of comments she made in March which sparked a furious backlash within her party.

The op-ed comes as Britain's exit from the EU is as uncertain as ever after talks with Labour's left-wing leader Jeremy Corbyn collapsed on Friday.