But John Holmes, the UN humanitarian chief, on Friday said the death toll was "unclear" and may not in fact ever be known. He said the figure of 20,000 had "no status".
Ban also the rejected claims that the UN had deliberately underestimated the toll earlier this week.
"I should emphasise that the final total is not yet known [and] most of these figures do not emanate from the UN and most are not consistent with the information at our disposal," he said.
However, Ban made it clear that whatever the total, the casualties in the conflict were "unacceptably" high.
The comments came as the Sri Lankan government seized a cargo ship organised by Mercy Mission, a London-based group, carrying more than 800 tonnes of food and medical supplies for Tamil civilians caught in the conflict.
The ship set sail from the British port of Ipswich to Sri Lanka via loading and customs in France. The Sri Lankan government has said that weapons could be on board and is holding the ship off the coast near Colombo, the capital.
Rohitha Bogollagama, the Sri Lankan foreign minister, told Al Jazeera: "Obviously any ship coming into territorial waters of a country has to be cleared in terms of its requirements for clearance.
"If any ship is trying to enter our waters, we have the right of arrest and we must inspect and that is a procedure. And in this regard, whatever action is taken, is a legitimate purpose towards establishing the intentions of the ones trying to bring the ship in.
"It could be threatening our national security or at the same time it could be a humanitarian exercise but let us examine that and let us respond accordingly."
Kristjan Guomundsson, a monitor on the aid boat, said: "I look at this as a possibility to open up a dialogue or connection between the Tamil diaspora and the Sri Lankan government.
"Because the Tamils in Europe, Canada and the US want to help with the IDPs [internally displaced persons] and Sri Lanka needs help because this is so huge. We're talking about 300,000 people.
"And I don't understand why the Sri Lankan government doesn't simply accept this and try to open up a channel between the Tamils abroad and themselves."
Demand for investigation
On Friday, rights group Amnesty International called on the security council to launch an investigation into possible war crimes on both sides in the conflict.
The group also said the council should demand that Sri Lanka give aid workers full access to displacement camps housing nearly 300,000 Tamil civilians.
The UN Human Rights Council decided last week not to investigate the civilian deaths in the war.
But Al Jazeera's John Terrett in New York says the problem with calls for a UN investigation is that the Sri Lankan government is democratically elected and many council members supported its defeat of the Tamil Tigers, whom they saw as a "terrorist" organisation.
Also, many council members have argued the war was an internal situation and not a matter for the council, which is why it took so long for it to even comment publicly on the conflict as it escalated this year, our correspondent adds.
The government routed the rebels last month following a decades-long conflict in which between 80,000 and 100,000 people are thought to have died.
The Tamil Tigers, or Liberation Tigers of Tamil Eelam (LTTE), took up arms in the early 1980s, seeking a separate homeland for ethnic Tamils in the north and east of the island country.
The Tamil Tigers had long accused the Sinhala-dominated government in Colombo of neglecting the Tamil minority.