Russia has criticised the summit, calling it disrespectful.
That comes after US president Barack Obama sparred with Russian president Vladimir Putin over the Syria crisis during their duelling UN speeches.
United States president Barack Obama sat down with more than 100 leaders at the United Nations to push ahead with a US-led campaign against the self-proclaimed Islamic State, or IS.
But Russia snubbed the summit, sending a low-level diplomat.
The fate of Syria’s President Bashar al-Assad is the key point of contention between the United States and Russia.
But the two countries’ leaders have agreed to work together to try to end the four-year war that has killed more than 240,000 people.
Opening the forum, Mr Obama said defeating IS, also known as ISIL or Daesh, in Syria will only be possible if President Assad surrenders power.
“Our military and intelligence efforts are not going to succeed alone. They have to be matched by political and economic progress to address the conditions that ISIL has exploited, in order to take root. In Syria, as I said yesterday, defeating ISIL requires, I believe, a new leader and an inclusive government that unites the Syrian people in the fight against terrorist groups.”
Russian president Vladimir Putin has maintained those trying to drive IS out of Syria must work with President Assad to do it, for both international legality and logistic reasons.
Mr Obama got support for his argument from British Prime Minister David Cameron.
“We’ll support the transition in Syria that, Barack, you spoke about and that we need to see so badly. We also will play a role in the propaganda war that we need to win, because, frankly, we need to call out ISIL for the mass executions, for the rapes, for the killing of innocent Sunni Arabs, while they’re selling oil and wheat to the Assad regime at the same time.”
The head of Australia’s delegation at the summit was Foreign Minister Julie Bishop.
She has reiterated Australia’s support for a political solution in Syria.
It comes after Australia had been accused of softening its stance on Bashar al-Assad, who is accused of committing war crimes.
Ms Bishop says Australia, together with a number of other coalition countries, is keen to keep all options in play.
“Geneva 1, that process of finding a political solution, was on the assumption that the Assad regime would fall, or Assad would be removed. Well, he’s still there. And so the political reality is you’re dealing with the situation as it stands today, and I believe that countries, including the United States and Britain and others, are considering what options are available, given that he’s still there.”
Ms Bishop told the forum everybody has a role to play in degrading, defeating and destroying IS and others committed to what she called violent extremism.
She outlined some of the measures she says Australia is taking to contribute.
“We’ve implemented a comprehensive package of domestic counter-terrorism measures, and we’re progressing the outcomes of Australia’s regional Countering Violent Extremism summit, held last June. We’re taking steps to disrupt the flow of foreign fighters from Australia and the funds that finance the activities of Daesh. However, my focus today is the coalition military effort. To address this threat and undermine Daesh influence, we must defeat the group at its source.”
Ms Bishop insists the coalition’s military campaign is making progress.
UN Secretary-General Ban Ki-Moon has asked all UN members to contribute to a new plan to combat extremism.
He says the plan would provide specific recommendations for individual and collective action to address the drivers of violent extremism.
As Mr Obama held the counter-terrorism summit, the United States also imposed sanctions against more than 30 IS leaders, financial figures, supporters and affiliated groups.
It is part of an effort to block the militants from the international financial system.