The chief prosecutor of the International Criminal Court Tuesday put foreigners fighting with Islamic State jihadists on notice that she was seeking ways of bringing to justice those behind crimes in Syria and Iraq.

Neither Syria or Iraq have joined the tribunal, but chief prosecutor Fatou Bensouda told AFP her office had jurisdiction over crimes committed in either country by citizens of the 124 nations which have signed up to court.

"We definitely have jurisdiction over those nationals," Bensouda told AFP, in an interview in the ICC's new headquarters on the outskirts of The Hague.

But she also revealed that apart from a handful of exceptions most foreign fighters "are not really at the top echelons of the ISIL structure," and that the "primary responsibility" for prosecuting them lay first with their national courts.

She was speaking a day after meeting with French Foreign Minister Jean-Marc Ayrault, who assured her France was "ready to cooperate" with the court and action could be "launched" if it concerns "nationals who are engaged in the war in Syria alongside Daesh," using another name for the Islamic State group.

France has been among countries upping the pressure at the UN Security Council to mandate the ICC to investigate war crimes committed by all sides in the five-year civil war in Syria.

The United States on Monday named a dozen Syrian generals and officers accused of leading attacks on civilian targets and running torture prisons, warning they will one day face justice.

"Those behind such attacks must know that we in the international community are watching their actions, documenting their abuses and one day they will be held accountable," said US ambassador to the UN Samantha Power.

But so far any attempts to agree to a resolution giving the ICC powers to investigate crimes in Syria have been vetoed by Russia, the main ally of Syrian President Bashar al-Assad, and China.

Set up in 2002, the tribunal based in The Hague is meant as a court of last resort to prosecute the world's worst crimes when national governments are unwilling or unable.

- Defections -

But the court, which is holding its annual meeting of state members in The Hague this week, is under a cloud amid a wave of defections by three African nations, which have accused the tribunal of being biased against the continent.

Russia also dealt the tribunal a blow last week when it withdrew its signature to the court's founding Rome Statute, prompting the Philippines to say it too may leave.

But Bensouda has vowed the row will not impede her work, saying the court was there "to ensure there is accountability for those people who perpetrate these crimes."

Her office will also soon decide on whether to open a full investigation into the conflict in Afghanistan, after determining that the Taliban militants, Afghan government forces and US troops all may have committed war crimes in the country.

Bensouda revealed an ICC team had just been in Afghanistan meeting with authorities there, and she was awaiting one more piece of information before making a final determination on whether to press ahead with a full-blown inquiry.

With many experts saying it would be unlikely that Washington would hand over any US personnel, Bensouda admitted it would be a complex investigation.

But she stressed: "We're still trying to complete the preliminary examination process, and in doing so we reach out. We reach out to all the parties that are part of the conflict there, including the international forces."