Mr Abbott said Australia would not waver. "The Australian government will be utterly unflinching towards anything that threatens our future as a free, fair and multicultural society," he vowed. "A beacon of hope and exemplar of unity-in-diversity."
Mr Abbott revealed more than 20 foreign fighters have so far returned to Australia from the battlefields of Iraq and Syria.
He congratulated Mr Obama on his leadership and said Australia was equally intent on taking the fight to the extremists in Iraq.
"Our goal is not to change people but to protect them; it's not to change governments but to combat terrorism," he said.
But Mr Abbott later stressed his government had still not made a "formal decision" to commit Australian forces in Iraq, despite pre-deploying 600 personnel.
He also stressed Australia had still not been asked to participate in action in Syria. Mr Abbott's speech came amid a series of one-on-one meetings with world leaders including Mr Obama, Indonesian President Susilo Bambang Yudhoyono, Japanese Prime Minister Shinzo Abe and French President Francois Hollande.
He will address the UN General Assembly on Thursday, celebrating Australia's role as a good international citizen.
The ongoing conflict in Ukraine, the Ebola epidemic in West Africa and the upcoming G20 summit in Brisbane are also on his agenda during his two-day visit.
Meanwhile, Mr Abbott's UNSC address drew some praise from an unlikely source: former PM Kevin Rudd. "He spoke well on Australia's behalf," Mr Rudd tweeted.
- AAP