Negotiations with gunmen holding two Cabinet ministers and about 80 of this Central American country's top business leaders hostage began in earnest today with the U.S.-backed government apparently taking a hard line.

Sources close to Honduran armed forces chief Gen. Gustavo Alvarez said he hopes to end the siege without bloodshed, but without giving in to the terrorists' demands, which include the release of prisoners and the removal of U.S. military advisers based here.

Although their hostages include members of the richest families in the country, all the terrorists' known demands are political rather than monetary.

The government of President Roberto Suazo Cordova and his Army under Gen. Alvarez have been seriously shaken in recent weeks by charges from a former head of the public security forces that Alvarez has become a pawn of Washington and is leading Honduras dangerously close to involvement in a regional war.

In this context, many leading Hondurans say privately that Alvarez cannot afford to make any major concessions to the guerrillas, but neither can he afford to precipitate a bloodbath by sending in his special Cobra antiterrorist unit to try to free the hostages.

The Reagan administration has been using economic and military aid to try to create here both a democracy and a powerful military force that could turn this once peaceful republic bordering on war-torn Nicaragua and El Salvador into a key stabilizing force in the region.

Guerrillas of the Cinchonero National Liberation Movement, which is closely linked to leftist rebels in neighboring El Salvador, stormed the Chamber of Commerce building here Friday night, taking 105 people hostage. Twenty were released and another three escaped. The Honduran treasury and economic ministers and the head of the Central Bank remain captive.

The main demand of the approximately 10 young men occupying the suburban building that once housed the U.S. Consulate in San Pedro Sula, Honduras's economic capital, has been the release of about 60 Salvadoran, Honduran and other Latin American leftist activists believed to be in jail or to have disappeared after being detained by government forces during the last two years.

The spark for the takeover appears to have been the reported arrest on Aug. 22 of Salvadoran guerrilla commander Alejandro Montenegro.

At a press conference yesterday, Honduran officials said Montenegro may already have been turned over to Salvadoran authorities under another name.

But in a broadcast this morning, Salvadoran guerrillas said on their clandestine Radio Venceremos that the release of Montenegro continues to be a key demand of the "Chinchoneros."