BEIRUT, DEC. 24 -- Looking dejected, hostage Terry Anderson appeared on a videotape released today, urging President Reagan to bring an end to the suffering of kidnaped Americans like himself. Anderson sent greetings to his family and friends on Christmas Eve, his third in captivity.

The pro-Iranian Islamic Jihad organization deposited the tape at the offices of an international news agency this afternoon without an accompanying statement. Delivery of Anderson's appeal today dashed hopes for a release that was expected during the Christmas holidays.

"Mr. President, I say again this cannot continue. There is a limit for how long we can last, and some of us are approaching their limit very badly . . . . Surely by now you know what must be done and how you can do it," Anderson said as he stood against a striped blue and white sheet.

Anderson, 40, looked healthy and wore a well-groomed beard, a beige sweater and glasses. The bureau chief of The Associated Press in Beirut, Anderson was abducted by gunmen in west Beirut on March 16, 1985, after a tennis match with a colleague. Anderson spoke quietly and in a hushed voice as he read from a prepared statement.

"To my government, I don't know what to say. I know that you are trying to get us out but I don't know exactly what you can do. I only know that it has not been enough or the right thing," he said. "Remember we are still here in our prisons and will remain here until you find a solution."

{In Washington, State Department spokeswoman Phyllis Oakley said, "We find it cynical that (Anderson's) captors have chosen to release this videotape on Christmas Eve, at a time when families traditionally gather together." She added, "All statements by hostages are made under the duress of their captivity. We continue to be deeply concerned for the health and well-being of all the hostages. They are not forgotten."}

"This is my third Christmas as a hostage," Anderson said. "Others have been nearly as long. Surely this is enough. It has to be. Our condition is not great," Anderson said despondently.

Islamic Jihad claims that it is also holding Thomas Sutherland, the dean of the Agricultural School of Engineering at the American University of Beirut, and three Frenchmen. The group has pressed repeatedly for the release of 17 Arab activists jailed in Kuwait since December 1983, following a wave of bombing attacks.

The liberation of French television lighting technician Jean-Louis Normandin last month set off speculation that all foreign hostages held in Lebanon would be freed by the end of the year.

But in his message, Anderson noted that there had been no progress in negotiations for the release of American hostages since David Jacobsen, the former director of the American University of Beirut hospital who was freed on Nov. 2, 1986. One day later, a Beirut weekly, Ash Shiraa, broke the news of the U.S.-Iranian arms-for-hostages swap.

Anderson said conditions for him and his fellow captives would be made better with an improvement of conditions for the 17 prisoners in Kuwait. "If something is done to improve their conditions, ours will, too," he said in a low voice.

Kuwait has publicly refused to link the 17 Arabs in its prisons to foreign hostages held by Iranian-backed groups in Lebanon. According to a senior Shiite militia source, usually well-informed on hostage affairs, an overall deal for release of the hostages was under discussion, but Kuwait has not agreed to the terms. Sources close to Shiite fundamentalists here say any such deal would have to include a pardon for the Kuwaiti prisoners.

Anderson pointed out that the three Americansfreed by Islamic Jihad in the past 2 1/2 years -- Benjamin Weir, Lawrence Jenco and Jacobsen -- did not gain their freedom through official U.S efforts, but through what he called unilateral and separate efforts.

Anderson's voice shook when he addressed his family. The American journalist, from Lorain, Ohio, has 10- and 2-year-old daughters, the younger of whom was born after his kidnaping. His father and a brother have died during his captivity.

"To my family, I love you and miss you very much," Anderson said. "I'm sorry we have to be apart again this Christmas . . . . I'm in good health, but tired and very lonely."

Addressing Reagan, Anderson said: "Mr. President, as you and all the Americans celebrate this Christmas with your families, think of us, think of our families. When the holidays and the New Year parties are over, you will go back to work . . . . Remember we are still here in our prisons, and we will remain here until you find a solution."

In addition to Anderson and Sutherland, other Americans are still being held hostage in Beirut. Beirut University College professors Alann Steen, Robert Polhill and Jesse Turner, as well as businessman Edward Tracy, Jack Reed, director of the Beirut International School, and Joseph Ciccipio of the American University of Beirut -- all kidnaped in Beirut -- are being held by two groups other than Islamic Jihad.

When French journalist Roger Auque was released last month, he said he had been held with English-speaking captives whose voices he could hear from his cell.