Mr Abbott has also spent the day in New York talking up trade and investment with business executives.
Signalling his "open for business" message, he rang the opening bell at the New York Stock Exchange before holding meetings with current and potential investors, some of whom are expected to put their money into new road and port projects to be rolled out in Australia.
Prime Minister Tony Abbott said he's ambitious for Australian jobs but won't be more ambitious when it comes to tackling climate change.
He began his day at the National September 11 Memorial, laying a wreath at a tree which was replanted after being found in the ruins of the World Trade Centre towers.
The prime minister solemnly walked around each of the 10 plaques representing the Australians who died in the terrorist attacks on September 11, 2001.
PM discusses climate change with UN chief
Prime Minister Tony Abbott meets UN chief Ban Ki Moon. (Photo: Karen Middleton, SBS)
Mr Abbott told reporters his government supported "strong action" on climate change and was investing $2.5 billion on emission cuts.
But he would not be modifying the government's plan.
"It's very important that every country take strong action to limit the rate of growth of emissions," he said.
"We know in Australia what we are going to do - we are going to get our emissions down by five per cent by 2020.
"We will be a good global citizen, but what we are not going to do is clobber our economy."
Mr Ban confirmed he would attend the G20 leaders' summit in Brisbane in November.
'US should not fear Asian century'
Mr Abbott also addressed a business lunch in which he argued the Asian century could exist alongside the American century.
"A rich China doesn't mean a billion competitors so much as a billion new customers," Mr Abbott said.
"Asia needs America involved. Asia needs America to succeed."
The prime minister will hold some private functions on Tuesday night (New York time).
On Wednesday he will attend a high-powered breakfast at the Council on Foreign Relations attended by senior corporate figures and former US Treasury secretary Robert Rubin.
He will then visit a technical school in Brooklyn before heading to Washington for meetings with US congressional leaders including speaker John Boehner, house minority leader Nancy Pelosi, house majority leader Eric Cantor and senate majority leader Harry Reid.
He is scheduled to meet with US President Barack Obama and Vice-President Joe Biden at the White House on Thursday.
PM ducks Hilary Clinton's comments on sexism
Prime Minister Tony Abbott says he won't be buying into Hillary Clinton's comments that former prime minister Gillard faced "outrageous sexism which should not be tolerated in any country".
Mr Abbott is in the US where he will meet US president Barack Obama tomorrow. The country is the final stop of Mr Abbott's 12-day four nation tour that also included Indonesia, France and Canada.
Speaking to reporters in New York, Mr Abbott acknowledged Ms Gillard faced "all sorts of difficulties" in office.
"But every prime minister faces all sorts of difficulties in his or her time as prime minister," he said.
Mr Abbott was the target of the now famous Gillard "misogyny" speech in federal parliament in October 2012.
He said he hoped to meet Ms Clinton while he was in the US.
"I think she was a highly creditable secretary of state, but beyond that I won't comment."
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