He called for greater efforts to achieve peace in Darfur and Somalia and urged a revival of negotiations to achieve a Middle East peace with Israel and Palestine living side-by-side in peace.
And he pledged to see the Afghans "through their long night" and stand as well with the people of Pakistan.
A day after about 100 heads of state and government in the largest-ever summit on global warming exchanged views on how to reach a new global accord to combat climate change, Ban again exhorted the leaders to "rise to the greatest challenge we face as a human family".
"This year I have traveled from the ice rim of the Arctic to the steppes of Mongolia," Ban said.
"I have seen, first-hand, the effects of climate change on our planet and its people."
The UN chief also urged leaders to "make this the year we agreed to banish the bomb," to address the "red flags of warning" about a global economic recovery and make a fresh push to achieve anti-poverty goals, especially reducing maternal and child mortality rates which remain very high.
The UN chief warned that "no nation, large or small, can violate the human rights of its citizens with impunity."
China 'opposes protectionism'
Leaders from 31 UN member states were on the list of speakers for the General Assembly on Wednesday.
"We should take responsible measures to counter the international financial crisis, firmly oppose protectionism and actively work for an early, comprehensive and balanced outcome of the Doha round of negotiations"
Hu Jintao, Chinese president
In one of the most keenly awaited speeches of the day, China's president urged countries to refrain from trade protectionism, days after a trading dispute with the US.
"We should take responsible measures to counter the international financial crisis, firmly oppose protectionism and actively work for an early, comprehensive and balanced outcome of the Doha round of [trade] negotiations," Hu Jintao said, in the first speech by a Chinese leader to the General Assembly.
His remarks came after US President Barack Obama imposed an import tariff of 35 per cent on Chinese tyres, in response to an appeal by a US trade union.
Hu said that efforts by China had helped shore up trading conditions during the protracted global economic and financial crisis, by keeping its currency "basically stable".
The Chinese president also said that nations should make a concerted effort against nuclear weapons proliferation.
"We call on the international community to take credible steps to push forward the nuclear disarmament process, eradicate the risks of nuclear weapons proliferation and promote the peaceful use of nuclear energy and related international co-operation," he said.
But Hu did not refer to Iran and North Korea, two countries with close ties to Beijing that have been subjected to UN sanctions over their nuclear programmes.
The Chinese leader's address to the UN came a day before Obama chairs a summit at the UN Security Council aimed at bringing fresh impetus to the Nuclear Non-Proliferation Treaty (NPT).