"I expect the year ahead to be among the most challenging in our history,'' he said.
"We need to pay less attention to rhetoric, and more attention to results, to getting things done"
Ban Ki-moon, UN secretary-general
"And I am sure that, together, we can make it one of the most successful .... We need to pay less attention to rhetoric, and more attention to results, to getting things done.''
The high-level session opened with speeches by Ban and the General Assembly president, and soon after by George Bush, the US president and other world leaders.
In a wide-ranging speech, Bush directed some of his harshest criticisms at the military leadership of Myanmar.
Bush announced the US would tighten economic sanctions against the country and urges other nations to apply pressure.
He added: "We will impose an expanded visa ban on those responsible for the most egregious violations of human rights [in Myanmar] as well as their family members."
Mahmoud Ahmadinejad, Iran's president, whose controversial views have provoked outrage and protests in the US, was due to take to the podium later in the day.
'Tragedy' in Darfur
Discussing the conflict in Darfur, where fighting combined with the effects of famine, has left at least 200,000 people dead and two million displaced since 2003, Ban said: "The government of Sudan must live up to its pledge to join comprehensive peace talks and implement a ceasefire."
Darfur armed groups are expected to hold talks with the Sudanese government in Tripoli on October 27 in an attempt to broaden the Darfur peace agreement signed in May 2006 to include groups which did not sign it.
A senior Egyptian diplomat said on Tuesday that the UN welcomed a
proposal by Egypt to send 2,500 troops to Darfur as part of a joint
UN-African Union force aimed at ending violence in western Sudan.
Ban, in the opening speech, also stressed peace in the Middle East is vital to the stability of the region and the world.
He said: "We know what is required: an end to violence, an end to occupation, the creation of a Palestinian state at peace with itself and Israel, and a comprehensive regional peace between Israel and the Arab world."
He called Iraq "the whole world's problem" and said the UN has an important role to play in promoting political negotiations and national reconciliation in the country.
In Afghanistan, he said, "we must work more effectively with our partners to deal with drug trafficking and the financing of terrorism."
Bernard Kouchner, France's foreign minister and his Iranian counterpart, Manouchehr Mottaki, were to meet on the sidelines of the session, diplomats from both countries said.
The meeting takes place against a backdrop of tension over Iran's nuclear program, which prompted Kouchner last week to say that France was preparing for war as a worst-case scenario.
Speaking to the general assembly on Tuesday, Nicolas Sarkozy, the French president, said allowing Iran to acquire nuclear weapons could destabilise the world.
He said: "There will be no peace in the world if the international community falters in the face of nuclear arms proliferation."
Iran insists its nuclear programme is for peaceful purposes.