The government says it is close to defeating the Tigers, but as many as 250,000 civilians may be trapped by the fighting on the Indian Ocean island nation, the BBC reported.
The call for the separatist Liberation Tigers of Tamil Eelam to discuss a surrender came as the International Committee of the Red Cross said civilians were fleeing a hospital that had been shelled for a fifth time in three days.
The ICRC says at least 12 people have been killed in the hospital in Puthukudiyiruppu, inside the 115 square miles of jungle in the north where the Sri Lankan military has cornered the separatist guerrillas.
"There remains probably only a short period of time before the LTTE loses control of all areas in the north," the joint statement from the United States, E.U., Japan and Norway said, according to Reuters.
Sri Lanka's military has encircled the Tigers and is confident it will win one of Asia's longest-running conflicts in which 70,000 people have been killed since 1983.
"The LTTE and the government of Sri Lanka should recognize that further loss of life -- of civilians and combatants -- will serve no cause," the joint statement said.
Fighting has escalated in the northeast, where government troops are pressing with an assault on the remaining patch of jungle held by the ethnic guerrillas. The government said the battle against the cornered Tigers was at a "decisive stage" and that it could not guarantee the security of tens of thousands of civilians trapped in rebel-held territory.
The government had promised safe passage but on Monday said it could not guarantee the safety of anyone still living among the rebels unless they entered an army-demarcated no-fire zone.
"People are on the move because they are looking for a safe place. But there is no safe place," ICRC spokeswoman Carla Haddad said from Geneva, according to the Agence France-Presse.
Also Tuesday, the government army said it captured an elaborate underground bunker complex believed to have been the home of the leader of the Tigers.
The two-story-deep bunker had sound-proof generators, air conditioning and medical supplies. It was hidden in a coconut grove in Mullaittivu district, the defense ministry said.
It described the site as the "main LTTE hideout" and "a major residential site" of rebel leader Velupillai Prabhakaran.
Pictures released by the defense ministry purported to show that Prabhakaran left behind a stuffed tiger, a paintball gun and a bottle of cognac.
At least 20 guerrillas were killed trying to defend the facility and another 12 rebels died in other clashes on Monday, the ministry said.
The whereabouts of Prabhakaran, 54, are not known, but Sri Lanka's military has said the Tiger chief may have already fled the island by boat.
Sri Lanka's government pulled out of a Norwegian-brokered truce a year ago, and a subsequent offensive has seen the LTTE's territory shrink from some 7,000 square miles.
Sri Lanka does not allow independent media free access to the island's conflict zone and to the camps housing those displaced civilians who have managed to flee the fighting.
"Reporters have already experienced physical attacks and intimidation, including the latest brazen assassination of renowned journalist Lasantha Wickrematunga," U.S. Sens. John Kerry and Richard Lugar said in Washington on Monday.
The United Nations, foreign governments and international and local rights groups have raised concerns over the safety of civilians while local doctors said a shell attack killed nine civilians at a hospital inside the conflict zone on Monday.
The government maintains that it has a policy of "zero civilian casualties."