The aircraft carrier USS Independence has been sent into the eastern Mediterranean Sea in response to escalating terrorist threats against U.S. facilities in Cyprus and Lebanon, administration officials said yesterday.

Also, ABC News said the carrier USS Eisenhower has been held in the eastern Mediterranean and other U.S. military forces put on heightened alert to deal with a possible terrorist attack, the Associated Press reported.

The Navy acknowledged that the Independence was steaming from Sicily toward Lebanon but declined to connect its orders with terrorist threats. Navy spokesmen said the ship will take part in a Egyptian-U.S. exercise next week.

But other officials said the carrier is being sent to the area in part because of intelligence reports that terrorists may attempt another attack against a U.S. installation, perhaps before Tuesday's election. The U.S. Embassy annex outside Beirut was badly damaged by a suicide truck-bombing on Sept. 20.

U.S. officials reported a high level of anxiety about possible attacks against the U.S. Embassy in Cyprus. They said they also have found signs of impending attacks in Beirut.

"If they try anything again, we'll be ready to respond," an official said.

The Reagan administration has threatened to retaliate against terrorists who attack U.S. personnel but did not respond to three earlier truck- or car-bombings in Beirut, largely because it could not pinpoint responsibility, officials said. Israeli and French forces last year conducted air raids against what they said were terrorist positions after their forces were attacked.

The Independence carries about 70 aircraft, including light bombers and fighter jets.

Administration officials have said they have seen disturbing signs of continuing terrorist activity since the Sept. 20 bombing. These have included vehicles apparently probing the defenses around the U.S. ambassador's residence outside Beirut and reports that explosives remain in the hands of those who planned the Sept. 20 attack.