The Prime Minister's campaign was widely criticised for not engaging with voters and stumbling on key issues.
Britain's opposition Labour leader Jeremy Corbyn said on Sunday there could be another election this year or early in 2018 after the vote on Thursday produced no clear victor.
But despite jubilation among Mr Corbyn's supporters at bloodying Mrs May' s nose, Labour MP Chris Leslie said the party should not pretend it achieved a "famous victory".
The outcome leaves May on Saturday battling to unite different factions in her party and reliant on the 10 seats of socially-conservative Northern Irish Democratic Unionist Party parliamentarians just nine days before the United Kingdom begins negotiating its departure from the EU.
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Johnson, one of the Conservatives' most popular politicians, tweeted that an article in the Mail on Sunday newspaper headlined "Boris set to launch bid to be PM as May clings on" was "tripe".
"I am backing Theresa May".
French doesn't think Brexit didn't really influence the outcome of the election for the Conservatives. Owen Paterson, a senior Conservative lawmaker, said "let's see how it pans out", when asked about May's future.
She said Brexit talks would begin on June 19 as scheduled, the same day as the formal reopening of parliament.
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May's party won 318 seats, 12 fewer than it had before the snap election, and eight short of the 326 needed for an outright majority. Three British women of Bangladeshi origin have also done very well on the Labour ticket and we congratulate them on their win.
After confirming on Friday that her top five ministers, including finance minister Philip Hammond, would keep their jobs, May must name the rest of her team, who will take on one of the most demanding jobs in recent British history.
"We will - obviously - amend the Queen's Speech".
But just hours later, DUP leader Arlene Foster was more reserved in her enthusiasm.
'Dead Woman Walking': Amid Election Fallout, Theresa May Stands On Shaky Ground
May's deal with the biggest party in the Northern Ireland Assembly is set to be discussed in her cabinet on Monday. But for now, Foreign Secretary Boris Johnson says reports of a plot to remove May herself is "tripe".
The former shadow chancellor labelled it an "OK result" after Mr Corbyn's party secured a higher-than-expected 262 seats and significantly boosted its vote share. "There's a possibility of voting it down and we're going to push that all the way", he explained. "Whoever it is, they are going to have to make deals with other political parties, and nearly every other political party that has an MP in the new parliament wants a softer version of Brexit", says French. Beleaguered British Prime Minister Theresa May was working to fill out the ranks of her minority government Saturday after an election that proved disastrous for her Conservative Party and complicating for Britain's exit from the European Union.