The US on Friday said it had no proof to support a claim from the Islamic State group that a coalition air strike killed an American woman it was holding hostage in Syria.

The jihadists named the woman as Kayla Jean Mueller, saying she had been buried under rubble after a raid by a Jordanian warplane in the Syrian city of Raqa, the militant group's self-proclaimed "capital".

But Washington refused to confirm her death while Jordan, still reeling from the brutal murder of one of its pilots by the jihadist group, rejected the claim as an "old and sick trick" to deter coalition strikes.

"The plane from the crusader coalition bombed a position outside the city of Raqa after Friday prayers," IS said in a statement posted on jihadist websites.

"No fighter was wounded but we can confirm that an American hostage was killed in the strikes."

The claim came as Amman said dozens of its jet fighters had struck IS, widening their campaign from Syria to include targets in neighbouring Iraq.

Jordan is part of the international coalition battling the Sunni extremist group, which has seized swathes of territory in Syria and Iraq and imposed an extreme interpretation of Islam on the areas under its control.

Jordan had vowed an "earth-shattering" response after the jihadists burned one of its fighter pilots alive and released a video of the gruesome execution.

Washington stressed it had not seen any proof that Mueller, a 26-year-old aid worker from Arizona, had been killed. IS did not post any pictures of a body with its claim.

"We are obviously deeply concerned by these reports. We have not at this time seen any evidence that corroborates ISIL's claim," said National Security Council spokeswoman Bernadette Meehan, using another acronym for IS.

Mueller's family described her as "extremely devoted to the people of Syria," adding that she had "devoted her career to helping those in need in countries around the world".

She was captured in August 2013 in Aleppo, they added in a statement.

'Old and sick trick'

Jordan's Foreign Minister Nasser Judeh denounced the IS claim on Twitter as "an old and sick trick used by terrorists and despots for decades: claiming that hostages human shields held captive are killed by air raids".

In Jordan thousands of people, including the nation's Queen Rania, marched on Friday to demand retribution against IS for the horrifying murder of pilot Maaz al-Kassasbeh.

"We are all Maaz... We are all Jordan," they chanted. Some held placards aloft that read: "Yes to punishment. Yes to the eradication of terrorism."

Queen Rania joined the marchers after weekly prayers at the Al-Husseini mosque, holding a portrait of the pilot with the words "Maaz the martyr of righteousness."

She told the BBC that the battle against IS "is absolutely Jordan's war", but that "to win it we need help from the international community".

Foreign Minister Judeh told CNN Jordan would hit the militants with all its might.

"We're going to go after them and we will eradicate them... We are at the forefront. This is our fight," he said.

The Syrian Observatory for Human Rights, a British-based monitoring group, said more than 30 IS fighters were killed in coalition raids Friday around Raqa, where it claims Mueller died.

US authorities have never given figures on the number of Americans kidnapped in Syria, sticking to a State Department policy of complete silence on any citizens held hostage abroad.

'Criminal propaganda'

Amman's government spokesman Mohammad al-Momani dismissed the jihadists' claim as "criminal propaganda".

"They have lied that our pilot is alive and tried to negotiate claiming he is alive while they had killed him weeks before," Momani told AFP.

IS offered to spare Kassasbeh's life and free Japanese journalist Kenji Goto -- who was later beheaded -- in exchange for an Iraqi woman, Sajida al-Rishawi.

The failed suicide bomber was on death row in Jordan for her role in triple hotel blasts in Amman in 2005 that killed 60 people.

But Jordanian television suggested Kassasbeh was killed on January 3, before IS offered to spare him and free Goto in return for Rishawi's release.

Jordan hanged Rishawi after IS released the video showing the murder of the pilot, who was taken prisoner in December after his F-16 crashed in Syria.

Jordan has conducted regular air raids across the border in Syria as part of the US-led campaign against IS.

American F-16 and F-22 jets have provided cover for recent Jordanian strikes, with additional support from refuelling tankers and surveillance aircraft, according to US officials.

Following Kassasbeh's capture, the United Arab Emirates withdrew from the coalition's strike missions over fears for the safety of its pilots, but a US official said on Friday that UAE flights were likely to resume "in a couple of days".

Jihadists have flocked to Syria since anti-government protests broke out in 2011 and escalated into a multi-sided civil war in which more than 200,000 people have died.