"We must galvanise global awareness and global action, with a special focus on Africa."
Ban said that a Green Revolution was needed in Africa with additional new resources.
He added that the intenational community had "not matched words with deeds" in reference to assisting Africa's development.
On the world economic crisis, Ban said: "We must think about how the world economic system should evolve to more fully reflect the changing realities of our time."
Ban also urged stronger action to combat the crisis in Somalia and highlighted the problems for the UN to meet deployment deadlines in Darfur, Sudan.
"If ever there were a call to collective action - a call for global leadership - it is now."
Al Jazeera's Sarah Brown, in New York, said meetings at the assembly would also address the Middle East conflict and the Iranian nuclear crisis, among other topics.
Brown said that with the recent conflict in Georgia and the situation in Iran would mean that the atmosphere at the assembly would be tense.
President Bush also spoke to the assembly on Tuesday, saying that he realised that other nations were watching the US to see how they deal with the economic crisis.
He said that he was confident that the US will act "in the urgent timeframe required" to prevent broader problems.
He did not ask for assistance from other nations.
Talking of the US$700 million bailout package proposed by his administration to fortify the US economy, Bush said: "I can assure you that my administration and our Congress are working together to quickly pass legislation approving this strategy."
Kristen Saloomey, Al Jazeera's correspondent in New York, said: "What was remarkable about [about Bush's speech] is what he didn't talk about so much.
"He did talk about Iran but only in passing. He didn't talk about Iran's president, Mahmoud Ahmadinejad."
Ahmadinejad, the Iranian president, and Ali Osman Taha, the Sudanese president, are also due to speak at the 63rd UN general assembly's annual ministerial session.