The justice minister of Trinidad and Tobago has told media that Jack Warner should get on a plane to New York and hand himself in.
The former FIFA vice-president was charged by the US last week over alleged corruption within world football's governing body.
Warner, who is an opposition MP in Trinidad and Tobago, was arrested with several other high-profile FIFA officials at the request of US authorities as part of their bribery investigation.
He was released on bail, pending a decision in his extradition case, which could take up to a year.
Warner has repeatedly denied wrongdoing and has threatened to divulge an "avalanche" of dirty secrets about FIFA and its outgoing President Sepp Blatter.
Asked by Sky News whether Mr Warner should travel to New York and hand himself in, Trinidad and Tobago's justice minister Prakash Ramadhar said: "That is what we are asking for".
He added: "If you love this country and you care about its reputation - and about the future of our children in particular - he, having been so highly held and loved by many, should set the right example.
"You can do the right thing even at this stage and in some way remedy the situation by taking responsibility, going to your trial or entering a plea if you are so minded to do.
"Let there be finality as soon as it is possible."
Trinidad and Tobago's communications minister Vasant Bharath earlier told Sky News that he thinks Warner's threat to release documents about FIFA show he is "playing for time".
"Mr Warner has been making these claims since 2008 when I was chairman of the party," Mr Bharath said.
"On many occasions he has threatened to bring all of these documents into a public forum but has not done so.
"He subsequently said he was joking and didn't have any and he has now come back with the same documents.
"I don't think he has the information which he says he has. He's bluffing. as he has always done. I think he's just really playing for time."
Warner refused to comment on the football corruption scandal earlier this week.
The call for Warner to hand himself in follow fresh allegations of corruption and bribery made about the contest to host the 2010 World Cup.
The Sunday Times claims that Morocco actually won the vote - but the process was rigged in favour of South Africa, which went on to hold the tournament in 2010.
Sky correspondent Enda Brady said: "This is shocking stuff. It centres around the whole voting process, the rights to hold the World Cup.
"We may well hear from FIFA later in the day."
