Russia believes US-led air strikes against jihadists in Syria should be carried out in coordination with Syrian authorities and in accordance with international law, Foreign Minister Sergei Lavrov said Friday.

Lavrov was speaking after the United States this week extended an air assault against the Islamic State (IS) group in Iraq to Syria with the support of five Arab countries.

"We believe that any action taken globally, including use of force, to overcome terrorist threats should be done in accordance with international law," he told reporters at the United Nations.

Russian President Vladimir Putin warned ahead of the strikes in Syria -- a Moscow ally -- that the offensive should not be carried out without the permission of Damascus, in a phone call with UN Secretary General Ban Ki-moon.

Lavrov reiterated that position.

"It's very important that such cooperation with Syrian authorities is established even now that it's an accomplished fact," Lavrov said.

"Excluding Syrian authorities from the struggle that is taking place... not only goes against international law but undermines efficiency."

US Secretary of State John Kerry had an "in-depth discussion" with Lavrov on the fight against IS earlier this week, a senior State Department official said.

"They agreed on the need to continue to work together and to assess the impact of the campaign against ISIL (IS) on the prospects for a wider settlement in Syria," the official said.