A French murderer who escaped from a Swiss prison this week, leaving a letter vowing to turn himself back in after taking a few days off, has kept his promise, authorities said Friday.

The 38-year-old man, who had been serving part of a 15-year sentence for the brutal murder of a prostitute at a semi-open Geneva penal institution, sparked an international manhunt when he failed to return on Sunday after spending the day working outside the prison.

In a letter addressed to his mother, he had explained that he needed four to five days of freedom and vowed to turn himself in once he had taken "some air".

"I will behave while I'm on the lam," he promised in the letter, his lawyer told AFP.

Keeping his promise, he walked back into the prison late Thursday, Geneva authorities said in a statement.

"As he himself had announced in advance, the resident presented himself last night to the establishment that he had failed to return to four nights earlier," the statement said.

The man, who was found guilty in 2005 of stabbing a prostitute 110 times, was denied an early conditional release in March.

Following his absence, the man will be transferred to a closed facility, but his sentence, set to last through 2019, will not be prolonged, authorities said.