Russian president Vladimir Putin has said the killing of a key opposition figure is a "disgrace" to Russia.

In televised remarks to interior ministry employees, Mr Putin condemned the death of Boris Nemtsov, who was shot while walking near the Kremlin in Moscow late on Friday.

While the Kremlin said on Saturday that Mr Putin had sent his condolences to Mr Nemtsov's mother, it was his first public remark on the subject.

"The most serious attention must be paid to high-profile crimes, including those with a political motive," he said.

"We must finally rid Russia of the disgrace and tragedy of the kinds of things we recently saw and experienced. I mean the audacious murder of Boris Nemtsov in the very centre of the capital."

No suspects have been detained yet in Mr Nemtsov's killing.