The UN estimates that up to 50,000 civilians are trapped in the fighting along the island's northeast coast.
'For civilians' sake'
Miliband said that international calls for a ceasefire were "only to save civilians" and not to help the LTTE, whose leader V Prabhakaran is making his last stand against the Sri Lankan military.
"No one in the international community has been calling for a ceasefire or to stop firing to save Prabhakaran," Miliband said.
"The calls have come because of the overwhelming concern with the well-being of the civilians."
According to the UN as many as 6,500 civilians may have been killed and another 14,000 wounded in the government's offensive against the LTTE so far this year.
Rajapakse pledged two days ago that air raids and attacks using heavy-calibre weapons would stop, but ground attacks have continued.
The LTTE accused the military of killing at least 11 people in the war zone on Tuesday, which the government denied.
John Holmes, the UN's most senior humanitarian official, left Sri Lanka earlier this week having failed to secure greater access for relief agencies.
After months of heavy fighting, the military says the LTTE is down to its last few hundred fighters.
The government has blocked most aid agencies from working in the north, and has put civilians who are escaping the fighting into camps guarded by the military.
Aid workers who have visited the camps have testified to food shortages, lack of sanitation, a desperate medical situation and chronic overcrowding.
Although the LTTE has been condemned for using civilians as human shields, the UN says both sides in the conflict may be guilty of war crimes.