David Cameron has said he respected and understood Sir Paul Stephenson's decision to resign as head of Scotland Yard.
The Prime Minister urged the Metropolitan Police to focus now on ensuring its investigations into phone hacking and corrupt payments to officers proceeded "with all speed, with full public confidence and with all the necessary leadership".
In a statement, Mr Cameron paid tribute to Sir Paul's career and record as Met commissioner.
"While I know that today must be a very sad occasion for him, I respect and understand his decision to leave the Met, and I wish him well for the future," the Prime Minister said.
"What matters most of all now is that the Metropolitan Police and the Metropolitan Police Authority do everything possible to ensure the investigations into phone hacking and alleged police corruption proceed with all speed, with full public confidence and with all the necessary leadership and resources to bring them to an effective conclusion."
Mr Cameron said Sir Paul had had a "long and distinguished career in the police" and thanked him for his service. "Under his leadership the Metropolitan Police made good progress in fighting crime, continued its vital work in combating terrorism, and scored notable successes such as the policing of the Royal Wedding," Mr Cameron said.
Home Secretary Theresa May said she was "sincerely sorry" that Sir Paul had decided to resign. She said there were "still serious issues to be addressed" in the circumstances of the current scandal, but added that the Met was operationally stronger than when he took over.
"Sir Paul has led the force through difficult times and, although current circumstances show there are still serious issues to be addressed, I believe the force is stronger operationally today than it was when he took over," she said.
Ms May is due to make a statement to the Commons which was scheduled before news of Sir Paul's resignation.
She had been due to report back to MPs on the Met's relationship with former News of the World deputy editor Neil Wallis.