FIFA is due to choose between the three-way "United2026" bid and one from Morocco at a congress in Moscow on June 13.
The three presidents said theirs was a technically sound, low-risk bid that featured state-of-the-art facilities, operational certainty and the promise of riches to fill FIFA's coffers.
They shrugged off any suggestion of anti-U.S. sentiment stemming from a probe in which U.S. prosecutors have brought corruption, racketeering and money laundering charges against 42 people and entities and described a culture of corruption around the awarding of media and marketing rights to soccer games.
The bid may also have to contend with irritation in several African and Middle Eastern countries at U.S. President Donald Trump's immigration policies.
"This is not geopolitics," Cordeiro told the call. "We are talking about football and what, fundamentally, at the end of the day, is in the best interest of football and our football community, and we've had no backlash.
"Our vision is a very simple one. We offer FIFA an unprecedented united opportunity to stage the 2026 World Cup. We believe strongly that this decision will be made on its merits."
But it may not be that simple.
Chicago was widely seen to have the best technical bid in the race to stage the 2016 Summer Olympics, but was eliminated in the first round of voting -- the victim of anti-American sentiment and disputes with the International Olympic Committee.
United2026 officials said they sensed no reluctance by delegates to award a World Cup to a country where they might be subject to subpoenas and wire taps by U.S. legal authorities.
(Editing by Kevin Liffey)