Islamic State has claimed responsibility for an attack on a traffic police post outside Moscow on Wednesday in which both attackers were killed, calling it revenge for Russia's aerial bombing campaign in Syria, reports Reuters.

The militant group made the claim via the Amaq news agency, which it regularly uses to issue statements, and released a video in which the purported attackers said they wanted to take revenge for Russia killing Muslims in the Middle East.

Russia has been bombing militants in Syria since September last year, part of a military campaign in support of President Bashar al-Assad.

Islamic State called on its members to carry out jihad or holy war in Russia in a YouTube video last month, after which the Kremlin said such threats would not affect its fight against international terrorism.

"We have taken the path of jihad on the orders of our Amir Abu Bakr al-Baghdadi," one of the purported attackers said on the video released by Amaq, speaking in a mix of Arabic and Russian. The video named the attackers as Uthman Mardalov and Salim Israilov.

"We have called this operation 'revenge operation'. Revenge for you bombing our brothers, because you kill our brothers every day in Syria and Iraq. ... This will be the start of everything that will come to you."

Russian investigators said on Wednesday that two unidentified people armed with a firearm and two axes had attacked a traffic police post outside Moscow.

One of them was shot dead while attacking the post, while the other was killed when he tried to put up armed resistance, the Investigative Committee said in a statement.

Two police officers were wounded in the attack, one seriously.