Defence Secretary Sir Michael Fallon has resigned, saying his behaviour may have “fallen short” of the standards expected by the UK military.
It follows claims of past behaviour – the BBC understands his decision was not related to new or specific claims.
The PM said she appreciated the “serious manner” in which Sir Michael had considered his role.
Theresa May also praised the “particular example you wish to set servicemen and women and others”.
‘Below high standards’
In his resignation letter, Sir Michael said: “A number of allegations have surfaced about MPs in recent days, including some about my previous conduct.
“Many of these have been false but I accept that in the past I have fallen below the high standards that we require of the Armed Forces that I have the honour to represent.”
In response Mrs May accepted his resignation and paid tribute to “a long and impressive ministerial career – serving in four Departments of State under four prime ministers”.
The resignation comes a day after a spokesman for Sir Michael confirmed that he was once rebuked by a journalist, Julia Hartley-Brewer, for putting his hand on her knee during dinner in 2002.
The spokesman had said Sir Michael apologised when it happened.
Following a range of recent allegations, including claims of a lack of support for those making complaints, Mrs May had written to party leaders calling for the “serious, swift, cross-party response this issue demands”.
The prime minister said a “common, transparent independent grievance procedure” for all those who work in Parliament was needed and that it “cannot be right” for policies to vary between parties.