The plea came as Ban Ki-moon, the UN secretary-general, telephoned Mahinda Rajapaksa, Sri Lanka's president, to discuss the plight of an estimated 100,000 civilians trapped in the zone.
The UN has said that between 150,000 and 190,000 civilians remain in the "no fire" zone, a 20sq km coastal strip in the island's northeast, which Colombo says is the only remaining area of LTTE territory.
The pro-rebel TamilNet Web site said on Thursday that shelling by the military
killed 129 civilians inside the safe zone the previous day.
But Anura Yapa, Sri Lanka's media minister, rejected the allegations.
"Our forces have not fired into that zone," he said.
"We don't want to shell that area. Our aim is to rescue the people from the LTTE [Liberation Tigers of Tamil Eelam]."
The "no fire" zone was established by the government to provide a place of refuge to civilians caught up in the fighting.
The UN believes that dozens of people are dying there every day.
The government says that between 30,000 and 40,000 civilians remain in the "no fire" zone, after more than 23,000 people fled the region last month.
Sophie Romanens, from the International Committee of the Red Cross, told Al Jazeera that civilians had fled to the "no fire" costal area to escape fighting and to find food and medicine over the past few weeks.
"Our concern now is that the area has been regularly affected by fighting. And now ... we have growing concern for their [the civilians] safety and well-being," she said.
"It is an area which is now full of people - one shelter next to the other. And the fighting is very close. These people are completely dependent on aid from the outside."
In the latest development, the Sri Lankan defence ministry said on Friday that troops were setting up "rescue points" just outside the "no-fire" zone to allow civilians to make a dash for safety.
"Troops continuously keep the civilians informed about the safe routes ... by removing terrorists blockades," the ministry said, referring to the LTTE.
"The rescue mission is also supported by limited offensives by troops to make room for the hostages to come out."
Soldiers had yet to move into the so-called safe zone but "we are very close to the border of the no-fire zone", Udaya Nanayakkara, the defence ministry spokesman, said.
The Sri Lankan military said recently that troops had taken the village of Puthukkudiyiruppu - the last territory held by the LTTE apart from the "no fire" zone - where they recovered 250 LTTE bodies.
The LTTE has not commented on the claim, which cannot be independently verified because journalists are prevented from entering the conflict area.
The LTTE has been fighting for an independent Tamil homeland in the north of Sri Lanka for more than 25 years.
More than 70,000 people have died in the civil war.