KABUL — Afghanistan's Taliban insurgents on Monday said an abducted American professor was gravely ill and urged the U.S. to accede to their demands for his release and that of an Australian colleague.

Kevin King and Australian Timothy Weeks were taken at gunpoint outside the American University in Kabul more than a year ago and later appeared in a January video tearfully asking President Donald Trump to exchange them for militant prisoners.

"We have periodically tried to treat and cure him, but since we are facing a war situation, we do not really have access to health facilities to provide him complete treatment," Zabiullah Mujahid, a spokesman for the Taliban, said in a statement.

Mujahid said King suffered from heart disease, kidney problem and swollen feet and the Taliban would hold the U.S. government responsible if anything happened to him.

He said the Taliban had presented to the United States its demands for releasing the pair, but did not reveal what they were.

The U.S. embassy in Kabul said they were aware of the Taliban statement.

"It is appalling that the Taliban continues to take and hold hostages in such dire circumstances," the embassy said in a statement of its own.

"We call for the immediate and unconditional release of Kevin King and all other hostages. The U.S. government will never stop trying to recover them and other Americans held by criminal and terrorist networks around the world," it said.

In September 2016, the Pentagon admitted to mounting an unsuccessful rescue mission for the hostages.

Security analysts have said the pair are likely being held by the Haqqani network, a hard line Taliban faction that has masterminded a series of deadly attacks in Afghanistan and has been behind a number of abductions, including of recently rescued American woman, Caitlan Coleman and her Canadian husband Joshua Boyle.

The couple, along with their three children, was freed after five years of captivity in what Pakistan said was a rescue operation after they were brought on its side of the border several weeks ago.

After her release, Coleman said she was raped by the Haqqani network who she blamed for killing one of her babies during the captivity.

The Taliban categorically denied her allegation, saying she lost it in abortion and due to lack of access for medial treatment.