After releasing another 20 hostages on Saturday, including two foreign ambassadors and 10 Japanese businessmen, the guerrillas said that they were willing to leave the residence peacefully "through dialogue".
They made no mention of their erstwhile key demand for the release of hundreds of jailed comrades, something President Alberto Fujimori has said is out of the question.
In a telephone call from Europe to Reuters news agency in Lima, a Tupac Amaru spokesman, Isaac Velazco, spoke yesterday of "an intermediate solution" which did not have to include the release of all Tupac Amaru prisoners.
The wife of Nestor Cerpa, the leader of the hostage-takers, is said to be among the prisoners, serving a life term on terrorism charges.
On the government side, the chief negotiator, Domingo Pal-ermo, Peru's Education Minister, who met Cerpa in the besieged residence for the first time on Saturday, said there had been "advances towards a solution of this crisis".
He was commenting specifically on the release of the 20 hostages, which left the rebels with 83 captives from the original 500-plus they took when they stormed a diplomatic cocktail party on 17 December.
The 20 or so guerrillas appear to be pruning their captives to a manageable number, perhaps one or two busloads, with a view to leaving the building for Lima airport and on to a jungle hideout or perhaps exile in a country such as Cuba.
The guerrillas still hold those they consider their most valuable hostages - Peru's Foreign Minister, Francisco Tudela, senior police and military officers, Supreme Court judges, congressmen and Mr Fujimori's brother Pedro.
The apparent softening of positions on both sides came amid reports that US Swat assault team experts were advising their Peruvian counterparts on how a hostage-freeing raid might work.
Americans were also reported to be analysing conversations within the ambassador's residence, picked up by bugging devices outside.
President Fujimori has taken a tough line publicly but he is said by diplomats to be making concessions in the talks involving Mr Palermo.
The key mediator appears to be a Peruvian bishop, Juan Luis Cipriani, from the city of Ayacucho, who has been visiting the besieged building every day since Christmas and appears to have defused the threat of a violent denouement.
In a communique read by a released hostage on Saturday night, the guerrillas criticised politicians and the media for billing their group as "a terrorist and genocidal band, which is absolutely false".
"Looking at the situation in the jails and the drama that the families of our imprisoned comrades have lived through, we think it will be understood that our petition should be heeded, and over time allow the achievement of an integral, lasting peace," the statement said.
That reflected earlier comments by Cerpa that Tupac Amaru wants to lay down its arms under an amnesty deal and then integrate itself into Peruvian politics as a populist party in support of the poor.
Many Peruvian intellectuals say that the Christmas hostage crisis was an accident waiting to happen. As in Mexico and other Latin American countries, emphasis on free-market economic policies has led to increased investment but has widened the gap between the rich and the poor.
This explained the rise of the Zapatista guerrillas and the People's Revolutionary Army in Mexico in the last three years, the intellectuals claim.
Government attempts to mobilise the Peruvian people in anti-Tupac Amaru marches brought only a few thousand out on to the streets, while the majority of the country's poor express sympathy with the guerrillas' goals, if not their methods.