Irish Foreign Minister Dermot Ahern has said Fifa is to reverse its rule that Northern Ireland players must carry British passports when going abroad.
Jim Boyce said the Irish FA had resolved the passport problem
Mr Ahern had raised the issue with world football's governing body, saying that players should be allowed to use a British or an Irish passport.
But his claim that his lobbying helped change the situation has been rubbished by the Irish Football Association.
The IFA said it was solved by "Fifa dealing with football people".
IFA president Jim Boyce added that politicians had made the the process more difficult.
"We had political interference in this which Fifa were very annoyed about," he said.
"What annoyed me was that the politicians didn't have the decency to come to the IFA and speak to myself or the chief executive over this issue, which we were aware of.
"I have also been annoyed because there has been an inference made of sectarianism within this organisation.
"I think everyone out there knows the tremendous work the IFA has put in to eradicate sectarianism from our game."
However, Mr Ahern claimed that Fifa had been guided by the Good Friday Agreement.
"It would appear now that they're going to reverse their decision," he said.
"They're going to accept that players from Northern Ireland can hold either a British or an Irish passport and travel on these as long as the Irish Football Association certifies the eligibility of the players involved.
"It looks as if administratively they have now gone along and accepted the whole premise on holding passports under the Good Friday Agreement."
The SDLP and Sinn Fein have also welcome the apparent u-turn by Fifa.
"Young footballers from the north will now have the opportunity to travel with the Northern Ireland soccer team on a passport of their choosing," the SDLP's Pat Ramsey said.
Sinn Fein's Martin McGuinness said: "I am happy that it now appears that Fifa are to recognise the demands of the Good Friday Agreement."