US wrestlers plan to be at next month's World Cup in Iran, despite that country's claim that it would ban American visitors in retaliation to President Donald Trump's controversial immigration order.

The US freestyle team's participation in one of the most prestigious wrestling events has been in doubt, given the fallout from Trump's executive order last week to ban travellers from seven Muslim-majority countries, including Iran.

The two nations have long had a congenial relationship in wrestling, but Iran said on Saturday that it would stop American citizens from entering the country, in retaliation to what it called "hostile policies" of the US government.

But USA Wrestling, which has a long tradition of competing with nations that may not have a strong relationship between their governments, said it still plans to send a delegation of 13 athletes, two coaches and a support staff to the February 16-17 in Kermanshah.

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"This tour continues a long history of goodwill and co-operation between the United States and Iran through wrestling, which is an impressive example of diplomacy between the people of these nations through sport," USA wrestling executive director Rich Bender said.

"This is an important international competition and we look forward to competing against the world's best wrestling teams."

While Iran has not backed off its claim to ban US visitors in retaliation to Trump's move, USA Wrestling told Reuters their contacts within the Iranian wrestling federation have said a committee has been formed in the foreign ministry to look at the World Cup.

"We're hopeful wrestling again will transcend politics," said Bender. "It's an important competition for us and seven other nations."

USA Wrestling said it sent the first American sports team to compete in Iran in nearly 20 years in 1998, when freestyle wrestlers competed in the Takhti Cup in Tehran.

American wrestlers have competed in Iran for the Takhti Cup nine times, while USA Wrestling said it has hosted teams from Iran in the United States 16 times since the 1990s.

By executive order on Friday, Trump banned immigration from seven Muslim-majority countries - Iran, Iraq, Syria, Libya, Somalia, Sudan and Yemen - and temporarily halted the entry of refugees.

The ban has angered many in the world of sports and even left some athletes uncertain of their ability to travel outside of the United States.