A Conservative former cabinet minister has warned his party against the "chaos" of a leadership contest as it could further delay resolving Brexit matters.
Owen Paterson said Theresa May was right "despite all the disappointments" to try to find a way to govern with the support of the Democratic Unionist Party given that the Tories won the most seats and most votes.
But the MP was less sure about how Mrs May could continue to rule in such a manner, saying "let's see how it pans out" when asked.
Speaking on BBC Radio 4's Today programme, the former Northern Ireland secretary told broadcaster John Humphrys: "We are nine days off from the Brexit talks starting, we've had two horrific security incidents, and to cast the Tory Party into yet another leadership contest I think would be very unwise.
"John, personally I wouldn't go and do it - I tempt you to go and talk to Brenda in Bristol..."
Mr Humphrys intervened: "She won't talk apparently, she's refusing all interviews. I don't know what that tells us of the state of the nation."
Asked how long Mrs May would stay as PM, Mr Paterson replied: "Let's see how it pans out. There is an immediate problem to get a government fixed which has a workable majority so we can begin to work on Brexit.
"This is coming down the track, the train is approaching and we have to get that resolved.
"There has to be the Great Repeal Bill put through the Commons, and our neighbours want to know how the form is going to be.
"The other mega issue which came up the whole time, quite rightly, is the issue of right of abode for the EU citizens living here and our citizens living on the continent."
He said Mrs May and Brexit Secretary David Davis had made clear this issue was a priority, adding: "We want to get that resolved as rapidly as possible and to have the chaos and uncertainty of a leadership contest would put the whole issue on hold and I think that's really bad for the stability, not least because of the whole economics looking ahead, with the pound dropping and everything else.
"So I think she's right - despite all the disappointments, she's got the most seats, she's got the most votes by a long way and she's right to sit down and try to work this through."
Former Tory health minister Nicola Blackwood, defeated by the Liberal Democrats in Oxford West and Abingdon, said "no party has been a winner" at the election.
On Mrs May's future, Ms Blackwood told the same programme: "She has to have the right team around her but they need to support her and make sure they put aside partisanship right now because it's about making sure we survive the security challenges we face but also the Brexit negotiations."
Former Tory minister Gavin Barwell, who lost his Croydon Central seat to Labour, earlier said: "I don't think you can call a result where you have got a vote share up at nearly 43% disastrous."
Reminded that the party had lost seats, Mr Barwell replied: "I'm not trying to pretend it's a triumph, clearly we didn't get the result we hoped to get. I'm just putting on record that she did better than (John) Major."
Asked if Mrs May has the authority to run the party and country, Mr Barwell said: "I believe there's a will in the Conservative Party to get behind her and support her.
"I think she's the best person to take Britain into these crucial Brexit negotiations that are going to be so important to the future of the country."
Former Tory leader Lord Hague said "very serious lessons" had to be learned by the party but warned against a leadership contest.
Writing in The Daily Telegraph, he said: "An overwhelmingly strong position at the time of the local elections on May 4 was turned into serious losses by June 8.
"The awful truth is that no party has given up such an advantageous situation with such speed in the modern electoral history of our country.
"Very serious lessons will have to be learnt from that.
"The Conservative campaign was strong on honesty and realism, but the next time the party enters a general election it will need to be just as strong on hope and vision for the future - and there's no reason it shouldn't be."
Stressing that a leadership battle was unwarranted, Lord Hague said: "Voters do not want further months of uncertainty and upheaval. They want to see ministers getting on with the job, while acknowledging democracy and their constrained circumstances."
A majority (59.48%) of Tory members now believe Mrs May should resign, according to a snap survey by the ConservativeHome website, while 36.66% of the 1,503 respondents believe she should stay on.
Former minister Ed Vaizey indicated that Tory MPs were actively discussing Mrs May's position using the WhatsApp messaging system.
Asked if there were phone calls being made between Tories about the next leader, Mr Vaizey told the BBC: "That's so 20th century. It's all on WhatsApp."
He added: "We all talk on WhatsApp ... lots of MPs are in lots of different groups."
Mr Vaizey said he hoped the election result would soften Mrs May's stance on Brexit, adding: "I hope in the next few days we will see a clear acknowledgement that a 'no deal is better than a bad deal' is off the table, that we are going for a Brexit that is going to secure jobs and investment."