"The Syrian authorities must open without any preconditions to humanitarian communities," Ban told reporters at the UN headquarters.
Amid reports of Red Cross convoys being blocked in the protest city of Homs, Ban told the UN General Assembly that "civilian losses have clearly been heavy. We continue to receive grisly reports of summary executions, arbitrary detentions and torture."
In Homs and other cities, people are trapped in their homes without food, electricity, medical care and cannot bury their dead, Ban said. "People have been reduced to melting snow for drinking water."
Syria has refused to let UN humanitarian chief Valerie Amos into the country, but Ban said the United Nations still hoped to persuade Assad to let Amos make an aid assessment.
"Why are they afraid of receiving the head of UN humanitarian department? We are ready to mobilize on this, we do not have access. So that is priority number one at this time," he said.
"We are pushing hard to have Valerie Amos visit Syria as soon as possible," and Syrian statements had indicated a visit could still be arranged, Ban said.
Syria's UN ambassador Bashar Jaafari again denied his country had blocked a visit.
He insisted that the Damascus authorities were waiting to set a date for a visit, but gave no indication of when Amos might be let in.
Speaking after Ban at the UN General Assembly, the Syrian ambassador stressed what he called his "long friendship" and "personal respect" for the UN leader -- but went on to give a 45 minute attack on Ban and the United Nations.
Jaafari said Ban's report "leans more toward increasing tensions than working toward a solution."
He accused the United Nations of "duplicity" by calling for efforts to bring the Syrian government and opposition together while using information from "countries which are open enemies of Syria."
Ban had given "an aggressive, virulent and slandering speech" while at the same time proposing to send former UN secretary general Kofi Annan as an envoy to Syria, the envoy added.
The UN leader's comments "will be interpreted by the armed groups as a legal cover to be able to act in a criminal fashion."
"Most of Syria is living normally," he added and the government was "sparing no efforts" to get services to people.
The ambassador hit out at Libya for offering $100 million to help Syrian opposition groups, and at Saudi Arabia's UN envoy, who gave a speech comparing events in Homs to the Srebenica massacre in Bosnia in the 1990s.
Jaafari called the Saudi speech "shameful" and added: "I hope not to be provoked further so that I do not make even more disrespectful statements."
Annan left New York on Friday to prepare his first talks with the Arab League next Wednesday. "From there he will try to visit Damascus as soon as possible," Ban said, adding that Annan will have a broad "flexibility" in dealing with Assad in a bid to obtain a halt to the violence.
The Arab League's plan for Syria calls on Assad to hand over powers to a deputy to organize new elections. But the UN leader indicated that Annan would not just press the Arab League plan.
"To have political dialogue with Syrian authorities, he should be given broader flexibility, a broader framework. This is what we have agreed, rather than sticking to any specific point" in the Arab League plan, Ban said.
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