The United States said there was no proof that the 26-year-old aid worker from Arizona had been killed.
Mueller's parents appealed to her captors to contact them and for her safe return, in a statement carried by NBC News.
"This news leaves us concerned, yet, we are still hopeful that Kayla is alive. We have sent you a private message and ask that you respond to us privately," said Carl and Marsha Mueller.
The Syrian Observatory for Human Rights said the US-led coalition fighting IS bombarded the Raqa area on Saturday for a second consecutive day.
More than 30 IS fighters had been killed in raids Friday around Raqa, said the Britain-based monitor.
A coalition statement said it had carried out a total of 11 air strikes against IS in Syria and 15 in Iraq during a 24-hour period up to Saturday morning, including in Raqa.
- 'Brutal terrorist organisation' -
It said one air strike struck multiple IS weapons storage facilities in the Raqa area.
Jordanian state media said its warplanes had launched new anti-IS raids Saturday, for the third consecutive day, without saying what the targets were.
Coalition partner UAE said an unspecified number of F-16s would be deployed in Jordan to support the Hashemite kingdom's military in the fight against "the brutal terrorist organisation" IS.
An activist in Raqa who asked not to be identified said unconfirmed reports indicate Mueller had been moved recently from a women's prison in the city to an IS camp farther east.
The camp "has recently been the target of intense coalition raids", he said. "At the moment, we cannot confirm whether she was killed in the raids."
Jordan -- still reeling from the brutal murder of pilot Maaz al-Kassasbeh -- rejected the jihadists' claim that its warplanes killed Mueller, calling it an "old and sick trick" to deter coalition strikes.
IS said none of its fighters was wounded in the raid, and it did not publish any pictures of her body.
The Jordanian military has said its fighter jets have launched dozens of strikes since Thursday, and that it would provide details to journalists on Sunday about the targets it says it has destroyed.
Foreign Minister Nasser Judah told Fox News this week the air force had targeted IS in both Syria and Iraq.
Interior Minister Hussein Majali said in remarks published Saturday that the burning alive of Kassasbeh by IS was a "turning point" in the kingdom's fight against extremism.
- Pilot safety fears -
After Kassasbeh's warplane crashed in Syria in December and following his capture by IS, the UAE withdrew from the US-led coalition's strike missions over fears for the safety of its pilots.
The official Emirati news agency WAM said Abu Dhabi Crown Prince Mohammed bin Zayed al-Nahayan, deputy head of the UAE armed forces, had ordered the deployment of the F-16s in Jordan.
"The initiative... reaffirms the UAE's unwavering and constant solidarity with Jordan and its leading role and immense sacrifices for the security and stability of the region as embodied by martyr and hero Maaz al-Kassasbeh," the agency reported.
US authorities have never given figures on the number of Americans kidnapped in Syria, sticking to a policy of complete silence.
Mueller travelled to the Syrian-Turkish border in 2012 to help refugees fleeing the civil war and was captured in Aleppo after leaving a Doctors Without Borders (MSF) hospital.
In northern Iraq, where Kurdish forces have pushed back IS, the remains of 23 men from the Yazidi religious minority were found in a mass grave, an official said on Saturday.
IS, a Sunni extremist group, has seized swathes of territory in Syria and Iraq and imposed an extreme interpretation of Islam on the areas under its control.