Sri Lanka's authorities have been under growing international pressure to allow time for tens of thousands of trapped civilians to leave the war zone safely, the BBC's Anbarasan Ethirajan reports from the capital, Colombo.
The military says it has captured the entire Tamil Tiger-held territory in the north and pushed the rebels into a government-designated safe zone for civilians.
Separately, Sri Lanka says it has stripped former mediator Norway of a role in any peace process.
'A good first step'
Sri Lankan troops fighting the Tamil Tigers have been told to fire only if attacked.
'Foreign Minister Rohitha Bogollagama speaks to the BBC'
A military spokesman told the BBC there had been no reports of any major fighting since the truce was called.
However, one soldier was killed and another injured in two separate incidents. The spokesman said the army did not retaliate.
He said only a handful of civilians had left the safe zone on Monday morning.
Our correspondent says it is unclear what the government's next move will be after the end of the two-day period.
The defence ministry says security forces have surrounded the no-fire zone on all three sides and troops are poised to enter the area to rescue civilians.
The pro-rebel TamilNet web site said the government's move was "a mockery of a ceasefire".
"The insulting 'festival diplomacy' announcement of [President Mahinda] Rajapaksa was aiming for the imprisonment of civilians by the state," it said, adding that the army wanted the "complete surrender of the Tigers".
The main message [to the Tigers] has been 'please end the suffering of the people by allowing them to leave if they wish to leave'
UN humanitarian envoy
"Rajapaksa knows very well that none of his expectations will take place," the web site said.
President Rajapaksa had called the truce after a cabinet meeting.
Foreign Minister Rohitha Bogollagama told the BBC that government forces would not engage in any offensive operations during the two-day Sinhala and Tamil New Year period.
UN humanitarian envoy John Holmes told the BBC he hoped the truce would mean more aid being allowed into the conflict zone.
"We would have liked a longer pause than this, a genuine humanitarian pause of a longer period than two days but this is a good first step," he added.
Mr Holmes said he had spoken to Tiger representatives and urged them to let civilians go.
"The main message has been 'please end the suffering of the people by allowing them to leave if they wish to leave'."
Thousands of people, mostly Tamils, have been protesting in Western capitals to demand a full ceasefire.
Demonstrators occupied the Sri Lankan embassy in Oslo for a brief time on Sunday, Norwegian police said.
The government later apologised for failing to stop the crowd, put at about 100.
However on Monday, Sri Lanka said Norway would no longer have any peace mediation role.
Norway helped broker a ceasefire in 2002. It later broke down and as the monitoring mission wrapped up its work at the start of last year, the new move is mainly symbolic.
Norway angered Sri Lanka recently by arranging a telephone call between a UN envoy and a Tamil Tiger representative.
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