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Four members of Iran's World Cup delegation have won appeals against having their visa applications for entry to the United States rejected.
But 11 members of the party will not be allowed to travel to the US when their team plays matches there.
Iran last week accused the US of denying visas to "integral" members of its national football team's backroom staff.
That was after officials in Washington said Iranian players had been given permission to travel to the country for the tournament.
Iran have already moved their World Cup base to Mexico over concerns stemming from the country being at war with the United States.
Of the 15 Iranian delegation members initially denied US visas, 10 submitted fresh applications after arriving in Mexico.
Four of those appeals were successful, it has been revealed. Those granted visas include a member of the team's technical staff working as an analyst and two officials from the federation's international department.
The remaining six applicants were rejected again. They include Iran Football Federation (FFIRI) president Mehdi Taj, one of the federation's vice-presidents, two team administrators responsible for day-to-day operations, a media officer and a security officer.
A second media officer chose not to reapply for a visa after the initial rejection.
Iran play New Zealand on 15 June in Los Angeles in their first game of the tournament, which is being co-hosted by Canada, Mexico and the United States.
They will return to the city to face Belgium on 21 June, before meeting Egypt in Seattle on 26 June.
The country's World Cup group-stage ticket allocation for supporters was revoked by US officials earlier this week, though Fifa has insisted it is working to "maximise opportunities for Iranian supporters to attend matches".
The FFIRI had previously presented Fifa with a list of 10 conditions for their participation in the World Cup, including allowing players, coaches and officials who have completed military service with the Islamic Revolutionary Guard Corps (IRGC).
US secretary of state Marco Rubio had said Iran's players will be welcome at the tournament but individuals with links to the IRGC could face entry restrictions.
Iran was not represented at a meeting of Fifa's annual congress in Vancouver in April after officials were turned away at the Canadian border, with Canadian officials citing the IRGC links of delegation members.
Fifa does not place a limit on how many people are in a nation's World Cup delegation, though it will only cover costs of up to 50 individuals.
The rejection of visas for the Iranian delegation members is not the only visa issue to arise at the tournament.
Fans from some nations have been barred from entry while Somali referee Omar Artan was denied entry to the United States to officiate at the World Cup.
Former Fifa president Sepp Blatter has criticised the body he led for 17 years over the visa issues, posting on social media: "A Fifa World Cup host country must guarantee two fundamental principles: the safety of the country - and the unrestricted entry of all qualified teams, officials and referees.
"The case of referee Omar Artan from Somalia is against one of these obligations. Fifa must never compromise the universality of football."
Blatter, 90, left the post following corruption allegations and was served with a six-year ban from all football, though a criminal case later cleared him of the charges.
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