"Our security forces have been instructed to end the use of heavy calibre guns, combat aircraft and aerial weapons which could cause civilian casualties," the statement said.
"Our security forces will confine their attempts to rescuing civilians who are held hostage and give foremost priority to saving civilians."
However, the Tigers' political head, B Nadesan, told the BBC Sinhala service that government artillery and jet bomber attacks were continuing to target civilians.
He repeated a call for international powers to put pressure on the Sri Lankan government to observe a ceasefire.
A government-run television station has broadcast images said to show the army helping civilians
The BBC's Charles Haviland in Colombo says until now the military and the government have said that they were not using any heavy weapons in this current stage of the fighting and had caused no civilian casualties.
This new statement, however, does appear to acknowledge that civilians have been harmed as aid agencies and the UN have been saying, our correspondent says.
He says the declaration may signal a radical change of tactics by government forces in the small war zone to try to avoid such casualties.
It may also mean that they feel their final military victory has been achieved, or nearly achieved.
Earlier on Monday, Sri Lankan troops launched a pre-dawn attack on Tamil Tiger-held areas in the north-east, a pro-rebel website reported.
Troops were firing from all sides and more than 10,000 civilians were at immediate risk, TamilNet said.
A military spokesman confirmed that troops were firing, but said they were doing so in self-defence.
No confirmation of the reports is possible as independent journalists are not allowed into the war zone.
On Monday the Chief Minister of India's Tamil Nadu state, M Karunanidhi, 85, went on indefinite hunger strike to demand a ceasefire in Sri Lanka. He called it off after the latest news from Sri Lanka.
John Holmes wants more UN access to the war zone
Sri Lanka's minority Tamil community has close cultural, religious and business ties with more than 50m Tamils in Tamil Nadu.
Meanwhile, the UN's top humanitarian official, John Holmes, has been in Sri Lanka for a number of days.
On Monday he said he thought there was little prospect of a ceasefire soon but that there should be more access to civilians affected by the fighting.
The UN says some 50,000 civilians remain trapped in a government-designated no-fire zone, but the army puts the number at 15,000.
Mr Holmes said he was "disappointed" President Mahinda Rajapakse had not agreed to allow a humanitarian mission into the war zone.
The rebels have been beaten back to a 12 sq km (5 sq m) area.
The Tamil Tigers have fought for an independent homeland for Sri Lanka's Tamil minority since 1983.
More than 70,000 people have been killed in the war, but that figure could now be far higher because of intensified fighting in recent weeks.
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