Warren Weinstein, 70, makes the emotional to President Barack Obama in a video released on several Islamist websites Sunday.
"My life is in your hands, Mr. President," Weinstein says in the video. "If you accept the demands, I live. If you don't accept the demands, then I die."
Weinstein, a development consultant, was abducted in August from his home in the Pakistani city of Lahore. In December, al Qaeda claimed responsibility for his capture.
Ayman al-Zawahiri, leader of the terror network, listed eight demands that he said, if met, would result in Weinstein's release. The demands related to issues in the Middle East, Pakistan, Afghanistan and Somalia.
"It is important that you accept these demands and act quickly and don't delay," Weinstein said in the video posted Sunday.
"U.S. officials including the FBI are assisting in the Pakistani-led investigation and cooperation with the Pakistani authorities in the investigation continues," the State Department official said Monday.
The State Department remains in close contact with the family, the official said, asking not to be named due to the sensitivity of the issue.
In the video, Weinstein makes references to Obama's daughters and to his own children.
He says he wanted to let his wife know he is "fine and well" in the video, which is less than three minutes long.
Al Qaeda's demands include the lifting of the blockade on movement of people and trade between Egypt and Gaza; an end to bombing by the United States and its allies in Pakistan, Afghanistan, Yemen, Somalia and Gaza; the release of anyone arrested on charges of belonging to al Qaeda and the Taliban; the release of all prisoners in Guantanamo Bay, Cuba, and American secret prisons and the closure of Guantanamo and the other prisons; the release of terrorists convicted in the 1993 bombing of the World Trade Center; and the release of relatives of Osama bin Laden, the founder of al Qaeda who was killed last year in Pakistan.
In August, Weinstein's kidnappers managed to overcome the three security guards who were protecting him.
As the guards prepared for the meal before the Ramadan fast, three men knocked at the front gate and offered food for the meal -- a traditional practice among Muslims during the holy month of Ramadan, according to the Lahore police.
Once the gate was opened, the three men forced their way in, while five others entered the house from the back, tied up the guards and duct-taped their mouths, according to the police.
They pistol-whipped the driver and forced him to take them to Weinstein's room, where they hit Weinstein on the head with a pistol and forced him out of the house and into a waiting car, the police said.
A police official said in August that three suspects had been arrested in Weinstein's kidnapping.
Weinstein was working for J.E. Austin Associates Inc., a consulting firm based in Arlington, Virginia.