(CNN) -- Tamil rebels in northern Sri Lanka faced a mid-day deadline to surrender or come under another onslaught from government forces.
A relative of a deceased serviceman wipes away tears Monday at ceremonies at a Colombo suburb.
Rebel Web site Tamilnet.com reported heavy shelling, rocket fire and gunfire. The rebels reported casualty totals exceeding 1,000.
"Hundreds of dead bodies and wounded civilians were still lying in Maaththa'lan and Pokka'nai," a Tamil correspondent reported.
U.N. Secretary-General Ban ki-Moon said Monday that he remained deeply concerned about the potential for large-scale casualties despite reports that thousands of civilians in Sri Lanka had been freed after being caught in an area between government forces and rebel fighters.
Sri Lanka's government has been battling the Tamil Tiger rebels in a civil conflict that has lasted nearly 25 years. The Tigers have been declared a terrorist organization by 32 countries, including the United States and the European Union. As many as 70,000 people have been killed since the conflict officially began in 1983.
There are an estimated 100,000 to 150,000 people trapped by the conflict in a 5-square-mile patch of land -- a government safe zone -- in the northeast of the country.
The Sri Lanka military announced Sunday that it had "punctured" the no-fire zone to free civilians trapped by nearby fighting, and warned Tamil Tiger rebels that more troop assaults would follow.
A video attributed to the military and played on Sri Lankan state television recently showed dozens of civilians wading across a lagoon in an attempt to flee the war zone. Some of the refugees were wounded and bleeding, while others were shown carrying children or injured relatives on their shoulders.
"In the light of the latest outflow of displaced persons, the U.N. is increasing its efforts to provide the required humanitarian assistance, and will continue to do all it can to ensure conditions fully reflect international standards," Ban said.
Ban condemned the continued use of heavy weapons near civilians and stressed the "imperative for U.N. staff to be allowed into the conflict zone to facilitate relief operations and the evacuation of civilians. It is also important to ensure the sustainable resettlement of these internally displaced persons as soon as possible."
On Friday, a pro-Tamil demonstration outside U.N. headquarters in New York attracted dozens of vocal supporters of the rebels. On Monday, French news reports said that 210 pro-Tamil protesters were arrested in central Paris.
A two-day pause in hostilities on April 12 allowed the United Nations and its partners to bring in aid and humanitarian supplies, but top U.N. officials called the brief cessation "inadequate."Sri Lanka's U.N. ambassador, H.M.G.S. Palihakkara, told CNN on Monday that his "government is deeply concerned about the plight of these civilians." The government intended to send more food and medical supplies to the conflict areas, according to the ambassador.