Two men have been detained over the murder of Russian opposition politician Boris Nemtsov, the head of the Federal Security Service (FSB) has announced.

Anzor Gubashev and Zaur Dadayev, both from the Caucasus region, were detained today, FSB Director Alexander Bortnikov said.

Russian investigators said there were suspected of organising and carrying out the murder.

The killing on a bridge within sight of the Kremlin shocked Russia.

The former deputy prime minister and veteran liberal politician, 55, was shot in the back four times on the night of February 27 as he was walking on the street with his girlfriend. He was buried in Moscow on Tuesday.

That the announcement was made on state television by the head of the FSB himself is a clear sign the Kremlin wants to be seen taking this case extremely seriously, the BBC's Sarah Rainsford reports from Moscow.

Bortnikov gave no details of how and where the suspects were detained, in the brief statement carried by Russia's state-owned Channel One, but he did say the investigation was continuing.

Neither of the men has yet been formally charged.

A source said to be familiar with the investigation told Russia's Interfax news agency the car allegedly used by the suspects was found rapidly and evidence gathered in the vehicle was used along with phone records to identify them, the source said.

Footage from security cameras had provided "sufficiently clear" images of the suspects, he added.

President Putin has publicly condemned the murder and called for an end to "shameful" political killings in Russia.

But leading opposition figure Alexei Navalny accused the Kremlin of ordering the assassination in order to cow the opposition amid Russia's mounting economic problems.

Russian investigators have publicly offered multiple motives ranging from Nemtsov's business dealings to his condemnation of the Charlie Hebdo attack in Paris.

Nemtsov was killed just days before a march he was organising against the war in Ukraine.

He had also been drafting a report expected to expose covert Russian military involvement in the conflict.

Some 50,000 people attended a rally near the Kremlin in protest at his death on March 1 and thousands turned out to pay their respects on the day of his funeral.

One Russian MP, Nikolai Kovalyov, told Ria-Novosti news agency that the key thing was to "find out who ordered this assassination".

Opposition activist Ilya Yashin said it was not enough to establish that the suspects had killed Nemtsov.

Writing on Facebook (in Russian), he said investigators needed to identify and arrest those who had ordered the murder.

"If those who ordered the murder are able to escape responsibility, the practice of political murders will definitely go on," he said.