Tense call between Trump and Australian leader strains longtime ties

* Trump promises to study 'dumb' resettlement deal

* Most serious rift in Australia-U.S. ties in decades -analysts

* PM Turnbull: Trump promised to honour asylum seeker deal (Adds meeting between Australian ambassador, White House officials)

By Jane Wardell and Roberta Rampton

SYDNEY/WASHINGTON, Feb 2 (Reuters) - U.S. ties with staunch ally Australia became strained on Thursday after details about an acrimonious phone call between its leaders emerged and U.S. President Donald Trump said a deal between the two nations on refugee resettlement was "dumb."

During a 25-minute phone call last Saturday with Australian Prime Minister Malcolm Turnbull, Trump accused Australia of trying to export the "next Boston bombers" under the agreement, the Washington Post reported.

The Post, which cited unidentified senior U.S. officials, said that Trump abruptly ended the call and told Turnbull that it was the "worst call by far" he'd had with a foreign leader.

The description of the call and a subsequent tweet from Trump promising to study what he called a "dumb deal" caused concern among lawmakers from Republican and Democratic parties.

"We always have reason to be concerned with respect to anytime our relationship with an ally might go sour. My hope is that it won't," Republican Senator Mike Lee told CNN.

"My hope is that we can achieve whatever objectives the president's willing to pursue in a way that won't damage the trade relationship or won't damage other aspects of our relationship," Lee said.

Representative Steny Hoyer, the No. 2 Democrat in the House of Representatives, urged Trump to apologize, while Republican Senator John McCain, chairman of the Armed Services Committee, said he called Australia's U.S. ambassador to express his support.

During former President Barack Obama's administration, the United States agreed to resettle up to 1,250 asylum seekers held in offshore processing camps on Pacific islands in Papua New Guinea and Nauru. In return, Australia would resettle refugees from El Salvador, Guatemala and Honduras.

The rift between Washington and Canberra that has developed over the resettlement deal could have serious repercussions. Australia and the United States are among five nations that make up the Five Eyes group, the world's leading intelligence-sharing network.

Later on Thursday, Trump told reporters at the White House he would "respect" the refugee agreement with Australia.

But Trump made it clear he was not pleased, saying it was an example of countries taking advantage of the United States.

"Why are we doing this, what's the purpose? So, we'll see what happens," Trump said.