Boris Johnson has accepted Matt Hancock's apology for breaching social distancing rules when he appeared to embrace his closest aide in a corridor in May.
The Sun published pictures of the married health secretary appearing to kiss close friend Gina Coladangelo.
Facing questions from reporters at a Westminster briefing, the prime minister's spokesman did not say whether Johnson had asked the health secretary to resign, nor if Hancock had offered the PM his resignation.
The spokesman also refused to address suggestions that Hancock had broken the law, repeatedly pointing reporters to the health secretary's statement.
Watch: Boris Johnson accepts Matt Hancock's apology for breaking social distancing rules
“You’ve seen the health secretary’s statement, so I would point you to that,” he said after being asked by reporters why Hancock remained in post.
“I don’t really have anything further to add.
“The health secretary set out that he accepted he had breached the social distancing guidelines and he has apologised for that.
“The prime minister has accepted the health secretary’s apology and considers the matter closed.”
Asked whether Johnson had “full confidence” in Hancock, the spokesman replied: “Yes.”
Hancock has apologised, saying: "I accept that I breached the social distancing guidance in these circumstances. I have let people down and am very sorry."
But he has refused to quit, saying: "I remain focused on working to get the country out of this pandemic, and would be grateful for privacy for my family on this personal matter.”
Two weeks ago Hancock was left red-faced after WhatsApp messages were leaked by former Downing Street adviser Dominic Cummings, which appeared to show Boris Johnson labelling him "f***ing useless".
Watch: Labour and Lib Dems call on Boris to sack Matt Hancock