By Aaron Bunch and Harry Pearl

SYDNEY (Reuters) - U.S. President Donald Trump has confirmed by telephone that his administration will honour a refugee resettlement deal with staunch ally Australia, Australian Prime Minister Malcolm Turnbull said on Monday.

The previous U.S administration had agreed to resettle a substantial number of the 1,200 asylum seekers, mainly from Afghanistan, Iran and Iraq, held in Australia's processing centres on remote Pacific islands in Papua New Guinea and Nauru.

But Trump's executive order on Friday, suspending his nation's refugee program, had cast doubt on the future of the deal, whose details and timing have never been made public.

"We discussed the importance of border security ... we also discussed the resettlement arrangement of refugees from Nauru and Manus, which had been entered into with the previous administration, and I thank President Trump for his commitment to honour that existing agreement," Turnbull said.

The two leaders spoke by telephone on Sunday, Turnbull told reporters in Canberra, one of a number of conversations the new U.S. president held with world leaders, including Russian President Vladimir Putin, German Chancellor Angela Merkel and Japanese Prime Minister Shinzo Abe.

U.S. Homeland Security officials have begun assessing the asylum seekers, although it was unclear when those found to be genuine refugees would be resettled. Under the deal, Australia will in return resettle refugees from El Salvador, Guatemala and Honduras.

Confirmation the deal would proceed came after Trump signed an executive order that put a four-month hold on allowing refugees into the United States and temporarily barred travellers from Syria and six other Muslim-majority countries, including Iran and Iraq.

In Sydney, up to 150 far-right protesters rallied on Sunday, holding placards supporting Trump and demanding a ban on Muslim immigration to Australia.

Turnbull did not comment on the Trump policy, saying, "It is not my job, as prime minister of Australia, to run a commentary on the domestic policies of other countries."

No Australian dual citizens of the countries affected by the order had yet sought consular help to enter the U.S., Turnbull said.

Australia's hardline immigration policy is a contentious issue that has drawn international condemnation from the United Nations and other rights groups, but which remains popular at home and has bipartisan political support.

Once fringe, far-right political parties like Pauline Hanson’s One Nation have gained wider backing, which sometimes spills over into calls for a ban on Muslim immigration.

Australia, a staunch U.S. ally, has been on heightened alert for attacks by home-grown Islamist radicals since 2014 and authorities say they have thwarted a number of plots.

(Reporting by Aaron Bunch and Harry Pearl in SYDNEY; Editing by Clarence Fernandez)