William Hague 'has Cameron's full support' over rumours
David Cameron supports William Hague "100%" following speculation about the foreign secretary's private life, the PM's spokeswoman has said.
Mr Hague issued a statement saying rumours of an "improper relationship" with a male aide were "utterly false" and his 13-year marriage was "strong".
On Thursday, Mr Hague said he had not been distracted by the furore and did not want to comment further.
But Tory peer Lord Tebbit said he had been "naive at best, foolish at worst".
The PM's spokeswoman said most people would feel sympathy for Mr Hague, whose special adviser Christopher Myers resigned on Wednesday following what Mr Hague described as "untrue and malicious" allegations.
She said Mr Cameron, who is on paternity leave, was not making any new statement on the issue but had given the foreign secretary his full backing throughout.
"We have always given William our 100% support. That was the case yesterday and it is the case today.
"The prime minister totally understands why William made the statement he did and he backs him 100%."
At a joint news conference with the German foreign minister on Thursday, Mr Hague said he was getting on with "some pretty important global issues" as foreign secretary - and said his work at the Foreign Office had not "missed a beat".
He said making the "very personal statement" had not been easy.
"I'm not going to expand on that today, my wife and I felt we'd really had enough of the circulation of untrue allegations, particularly on the internet," he said.
"At some point you have to speak out about that to put the record straight."
BBC political correspondent Carole Walker said the news conference had been an uncomfortable experience for Mr Hague - who later attended a cabinet committee in Downing Street.
She said both he and No 10 were clearly hoping that his public comments would draw a line under the matter.
In Wednesday's statement, Mr Hague said he had felt compelled to comment following 10 days of "press and internet speculation".
He said he accepted "in hindsight" he should have realised there might be speculation about the fact he and Mr Myers occasionally shared a twin hotel room during the election campaign.
"Neither of us would have done so if we had thought that it in any way meant or implied something else," he said.
Mr Myers had been "easily qualified" to be his special adviser, he said, rejecting any suggestions that his appointment was due to an improper relationship between the two as "utterly false".
He also disclosed that his wife had suffered a number of miscarriages in the past including one as recently as this summer, describing this as "immensely painful and traumatic" for the couple.
Conservative peer and former cabinet minister Lord Tebbit told the BBC Mr Hague had been "naive at best, foolish at worst".
And veteran Conservative MP John Redwood said the statement was "unusual" and suggested it had "invited people to comment" on the couple's private life.
"Let us hope this is now an end to the matter," he wrote on his blog. "Mr Hague himself now seems to understand that it was poor judgement to share a hotel room with an assistant."
However, the chairman of Mr Hague's constituency party said it had been a "brave statement". Christopher Bourne-Arton told BBC Radio 4's World at One programme: "The unfortunate thing was that some story or some rumour has been created by somebody who makes a living out of blogging, has nothing better to do, and so he had to nail it once and for all.
"The tragedy is that it was made necessary by this media feeding frenzy, and I rather wish they'd all go back into the slime pool from which they arose."
Labour leadership contender Ed Balls said he felt "sorry" for Mr Hague and his wife but doubted whether a public statement was the "wisest" course of action for him to have taken.
"I think it probably gives more credibility to some of these websites and to allegations which are not true," he said.
Public relations expert Max Clifford said Mr Hague had made a mistake by drawing attention to what were unfounded rumours and whoever was advising the foreign secretary had got it "totally wrong".
"The vast majority of the British public would have been totally unaware of this. Now everyone in the country is aware of it," he told BBC Radio 4's Today programme.
"It is damaging. It has taken a small problem and turned it into a huge problem for him. That's not good public relations."