Theresa May’s plan for a loose alliance with the Democratic Unionists to prop up her government was thrown into confusion on Saturday night after the Northern Ireland party contradicted a No 10 announcement that a deal had been reached.

A Downing Street statement on Saturday said a “confidence and supply” agreement had been reached with the DUP and would be put to the cabinet on Monday. But the DUP last night put the brakes on that announcement, saying talks were continuing, not finalised. The DUP leader, Arlene Foster, said “discussions will continue next week to work on the details and to reach agreement on arrangements for the new parliament”.

Following talks between May and the DUP last night, a second statement from No 10 clarified that no final deal had been reached. A Downing Street spokeswoman said the prime minister had discussed “finalising a confidence and supply deal when parliament returns next week … As and when details are finalised, both parties will put them forward.”

Earlier it emerged that angry Tory MPs had threatened to object to a formal coalition. The MPs had begun warning party whips they would oppose any formal deal, because of the DUP’s position on gay rights, abortion and climate change. The looser deal on offer would see the Northern Ireland party’s 10 MPs support the prime minister in key votes but not enter a closer pact with the Tories.

The decision to rule out a formal pact, which could make it harder for May to govern, comes after her trusted joint chiefs of staff, Nick Timothy and Fiona Hill, resigned following her shock failure to secure a majority in Thursday’s general election. May had been under pressure from ministers to sack the pair or face an immediate leadership challenge. Gavin Barwell, who lost his Croydon Central seat, has taken up the role of chief of staff.

May is fighting to keep the job she won less than a year ago. As the general election result emerged, senior Tories are understood to have contacted Boris Johnson to sound him out about launching another leadership bid should May be unable to continue. Friends of the foreign secretary dismissed any suggestion that he would try to force May out, stating that he was backing her decision to stay in post. “It is nonsense to suggest he is manoeuvring,” they said.

Boris Johnson tweeted on Saturday night that reports of a challenge were “tripe”.

Mail on Sunday tripe - I am backing Theresa may. Let's get on with the job — Boris Johnson (@BorisJohnson) June 10, 2017

The Observer has learned that the DUP was planning to dodge a row when negotiations began by avoiding the inclusion of any controversial social policies, such as opposition to gay marriage or abortion, in its so-called “shopping list” of demands to the Tories. Party sources said it would be seeking commitments from May that there would be no Irish unity referendum and no hard border imposed on the island of Ireland.

However, some Tories remained concerned that a pact would damage a brand they have spent years trying to detoxify.

“More and more colleagues are becoming distinctly uneasy about the idea of a formal pact with the DUP,” said one senior Conservative. “It is up to the DUP if they want to support a Conservative government and vote for various measures that we put through, but there is a feeling that we are damaged if we are seen to be entering into a formal agreement with a party whose views on a number of things we just don’t share.

“Why should we damage what we painstakingly built up through David Cameron’s work on personal issues, and indeed what the prime minister’s own instincts are, with any form of formal linkage with people who plainly have some views that the vast majority of Conservative MPs would not share?”

Nicky Morgan, an education secretary under David Cameron, said: “As a former minister for women and equalities, any notion that the price for a deal with the DUP is to water down our equalities policies is a non-starter.”

An online petition calling for May to resign rather than form a coalition with the DUP had attracted more than 500,000 signatures Saturday night.

The DUP is opposed to abortion and same-sex marriage. It has also appointed climate change sceptics to senior posts within the party. The former Tory cabinet minister Owen Paterson sparked alarm by suggesting that his party might have to enter into “a debate on further reduction of abortion times as medical science advances”. But it is understood that the DUP will argue that controversial issues such as gay marriage and abortion can be dealt with only in a Northern Ireland context by the Stormont assembly.

Ruth Davidson, the Scottish Tory leader, has expressed concern over the impact of a DUP deal on gay rights and other issues. But one DUP source said: “Someone is stirring the pot with Ruth, who we regard as a hero of the union.”

The DUP has been at the forefront of opposition in Stormont to legalising gay marriage and reforming the near-total ban on abortion in the region. Seeking a soft border would raise the question of whether or not the DUP backs the UK staying in the EU’s customs union. The party will also insist that there are no checks at English, Scottish or Welsh ports and airports on any citizens travelling from Northern Ireland after Brexit.

DUP sources said the list of demands would be similar to its 2015 “Northern Ireland” plan, when the party laid out its price for supporting either a minority Tory or Labour administration. That included more Treasury cash for Northern Ireland’s schools and hospitals. Also among the DUP’s conditions will be at least a 50% cut or the total abolition of air passenger duty in Northern Ireland.

Discussions between the DUP and the Conservatives will run parallel with negotiations this week involving all the main parties in Northern Ireland. The latter talks are aimed at restoring the power-sharing devolved government in Belfast. Writing in today’s Observer, Jonathan Powell, Tony Blair’s secret negotiator with the IRA after the 1998 Good Friday agreement, saidon Monday: “If Mrs May depends on the DUP– Ian Paisley’s party, not the old Official Unionists who used to work with the Tories – to form a government it will be impossible for it to be even-handed.”