US president Barack Obama has phoned Prime Minister-elect Tony Abbott to congratulate him on the Coalition's election win.

A spokesman for Mr Abbott says the pair reaffirmed the strong relationship between the two countries, and discussed the civil war in Syria.

Mr Abbott commended the president on a "fine speech" in relation to the continuing conflict in Syria, and reiterated Australia's willingness to do everything possible to be of assistance in political and diplomatic terms.

He said that if it was possible to chastise Syria without the use of force, then that would be welcome.

But Mr Abbott also said the United States would have Australia's strongest support if military force was required.

The two leaders also discussed the need to improve trade and investment links in the region, and agreed to work cooperatively towards the Trans-Pacific Partnership.

Mr Abbott also told Mr Obama that he looked forward to seeing him at upcoming summits.

Earlier this morning, US secretary of state John Kerry rang Coalition foreign affairs spokeswoman Julie Bishop and agreed to meet at the United Nations later this month.

Mr Abbott has spoken with a number of world leaders since Saturday's election win, including British prime minister David Cameron and Indonesian president Susilo Bambang Yudhoyono.

Yesterday he had a telephone conversation with Israel's prime minister, Benjamin Netanyahu, telling him he wants the strongest, closest possible relationship with Israel.