Mr Fujimori left open the possibility of an assault on the building if the 22 guerrillas did not surrender and free their 340 hostages. He refused the key demand of the Tupac Amaru members - the release of at least 300 of their jailed comrades.
He urged the guerrillas to hand their arms to mediators. "In that way, the possibility of the state using force would be ruled out." Observers noted that the wording left a commando assault very much still a threat, assuming the rebels do not surrender soon.
There was no sign of heightened military activity in the San Isidro suburb, but hundreds of commandos, police and armed plainclothes officers dotted the area. In the building, with the siege nearly a week old, conditions were described by a freed congressman as "almost a cruel joke", as Mr Fujimori tested the rebels' nerves.
Each guerrilla of the Tupac Amaru Revolutionary Movement (MRTA) is guarding 15 or so hostages - all men - locked in individual rooms. With electricity cut, the captives are in darkness at night.
Pictures released yesterday show the captives, including Peruvian ministers, foreign diplomats, Japanese businessmen and other dignitaries, lounging or sleeping on bare floors. Most looked exhausted. A few managed smiles.
An anxious-looking Peruvian Foreign Minister, Francisco Tudela, appeared to be in a kitchen with several other hostages. The Cuban ambassador to Peru was said to be suffering from a dislocated hip because of crouching on a floor but was refusing to abandon an embassy colleague, although the rebels gave him permission to leave. "He is in great pain," a Peruvian congressman, Javier Diez Canseco, released earlier in the week, said. "After the running water was restored, the generator ran out of fuel, so there was no power for the pump. It's a major hygiene problem. The hostages are using plastic bags as toilets."
The local head of the International Red Cross, Michel Minnig, spent a night in the residence, apparently to see if there was any reaction to Mr Fujimori's broadcast message. "Everything is normal. There has been no reaction up to now," Mr Minnig said when he came out yesterday.
A Peruvian university professor, Javier Sota Nadal, released on Friday, said: "We thought we could die at any moment." He said David Griffith, one of two Britons being held, had taken the role of "leader" of their room of hostages. "He was organising the distribution of food, water and toilet trips."
The hostages apparently had to resort to plastic bags when portable toilets allowed in earlier were full or in use.
Mr Griffith, in his mid-forties and manager of Lima's Hotel Las Americas, was born and brought up in Peru and has dual nationality. The other British hostage is Roger Church, 50, deputy head of the embassy here. The embassy has had no word on his condition.
In a message he sent by radio, permitted by the guerrillas, Mr Tudela said the rebels were serious, polite and did not swear. They had hurt no one. The Foreign Minister said it was vital for his colleagues on the outside to find a way to communicate directly with the rebels. The Education Minister, Domingo Palermo, was going to and from the building, with Mr Minnig, but the process of passing messages was slow. In another radio contact on Saturday, the rebel leader, Nestor Cerpa, promised gradually to release more hostages - "those not linked with the government".
Outside a police cordon, but within hearing of the hostages, a choir sang "The Little Drummer Boy" and other Christmas songs to lift their spirits. Two women who described themselves as "humble Peruvian citizens" walked up and down past dozens of film crews, carrying a Bible and a large cross and saying prayers. "We are praying for the Virgin Mary to bring us a Christmas miracle, a peaceful end for the hostages and their families," said one.
Yesterday thousands of people held a peace and solidarity march to the police cordon near the residence. They wore white ribbons, carried white balloons and sported "I love Peru" badges. Most were from official organisations, apparently part of a campaign by Mr Fujimori to show that he has public support. "A terrorist group cannot impose itself on 23 million people," he said in his broadcast.
Japan's Foreign Minister, Yukuhito Ikeda, who met Mr Fujimori and mediators here at the weekend, backed the Peruvian President's stand. Peru would need Japan's agreement for any assault on the residence, which is legally Japanese territory.