BOGOTA, COLOMBIA, AUG. 4 -- Peace initiatives by the Medellin cocaine cartel and its armed bands, seemingly aimed at forcing the incoming government of Cesar Gaviria into a softer stand on extradition of drug suspects, are gaining national support and worrying U.S. officials.

Gaviria, who takes office Tuesday, has said he will continue the all-out war against Pablo Escobar and the cartel pursued by outgoing President Virgilio Barco, but a recent poll shows that people oppose the government's get-tough policy by a 2-1 margin and are tired of the violence.

The cartel recently declared a "unilateral, indefinite truce" and requested that extradition of drug suspects to the United States for trial be made a topic of an upcoming constitutional convention. The offer, while not as explicit as its January offer to surrender in exchange for a halt to extradition, has generated widespread commentary.

Many analysts view the move as especially significant because it came the day after the government returned three towns on the outskirts of Medellin, all considered Escobar strongholds, to civilian rule after several months under unpopular military rule.

Wednesday, Fidel Castano, the leader of right-wing paramilitary groups linked to the cartel, published an open letter saying that he is willing to disband his forces if peace talks between the government and a group of Marxist guerrillas are successful.

The government denies there are any negotiations underway, but there is a widespread feeling in political circles that both sides are seeking to reduce tension in the hope of controlling the violence.

"It may be that soon these gestures . . . will be translated into tangible realities so the government that takes office in a few days can dedicate itself to building a Colombia that is more kind and just for all," an editorial in El Tiempo, the nation's largest newspaper, said Thurdsay.

"It concerns me that people think like that, because it plays right into where Pablo Escobar wants the government to be," said a U.S. official with expertise in narcotics. "I think it would be a great, great mistake for the government to make any move toward responding positively to those appeals."

Gaviria has responded to the trafficker's moves cautiously, saying in recent days that extradition should not be the primary instrument used to fight traffickers, and that his use of it would depend "on the situation of public order." His advisers say Gaviria is also aware of the political cost of carrying out the war, which is unpopular.

In a monthly poll of 615 people in the nation's four largest cities published Friday, 63 percent said they opposed Barco's tough, anti-dialogue narcotics policy, while only 37 percent supported it.

Political analysts say the reason for the lack of support is the violence generated by the conflict.

A recent study by Rodrigo Losada, a research specialist in Colombian violence, showed that the number of homicides here jumped from 15,672 in 1986, when Barco took office, to 23,312 in 1989, and is running at an even higher rate in 1990.

Losada said the 1989 totals give Colombia a homicide rate of 68.1 per 100,000 inhabitants, the highest in the world, up from 44.2 homicides per 100,000 people in 1986. As a point of reference, the United States has a homicide rate of 10.8 per 100,000 people.