Mahinda Rajapaksa, the Sri Lanka president, said in a statement on Sunday that people should be "given uninhibited freedom of movement".
Rajapaksa also urged the LTTE to surrender.
"In the true spirit of the season, it is timely for the LTTE to acknowledge its military defeat and lay down its weapons and surrender. The LTTE must also renounce terrorism and violence permanently," the statement said.
Mediators of Sri Lanka's peace process - the US, UK, Norway and Japan - on Friday urged the rebel Tigers to end the "futile fighting" and urged the military not to fire into the no-fire zone.
The Sri Lankan military denies shooting into civilian areas saying the allegations are Tiger propaganda.
It has also refused all calls for a ceasefire, saying the Tigers repeatedly have used them to regroup to fight another day.
The LTTE has so far rejected pleas to let civilians leave, insisting they were staying by choice.
The Tigers have been fighting since 1983 for an independent state in the north and east of the island for the Tamil minority, saying Tamils have suffered decades of marginalisation at the hands of governments dominated by the Sinhalese majority.
More than 70,000 people have been killed in the unresolved conflict to date.