Infantino said FIFA's judicial bodies operated "independently and autonomously" and that he had told Trump the Balogun case was subject to an ongoing legal process, even as the US President described the decision to reinstate the United States striker as "brilliant" after personally urging FIFA to review the case.
The affair has become the tournament's biggest controversy, drawing condemnation from European football body UEFA, which said FIFA had "crossed a red line", the Royal Belgian Football Association, several national federations as well as senior coaches, officials and politicians, with critics arguing FIFA had undermined confidence in its own disciplinary system.
It also prompted the Belgians, who play the US later on Monday for a place in the quarter-finals, to challenge Balogun's eligibility for the match but their appeal was rejected by FIFA.
The player was sent off for a tackle during the US win over Bosnia and Herzegovina, a punishment that usually carries an automatic one-match ban.
"He (Balogun) didn't do anything wrong and he is our best player," Trump told reporters at the Oval Office on Monday. "When they take your best player and say 'You can't play' it's very unfair."
"I think they made a really brilliant decision," Trump said. "I asked for a review. If they would not allow a top player to play I think it (the World Cup) would have had a big stain. I related that feeling."
Trump also questioned the quality of refereeing by Brazil's Raphael Claus, who had sent Balogun off, saying he was "a little bit suspect if you check his past." He did not elaborate.
Infantino later confirmed the call but said he explained to Trump that FIFA's judicial bodies operated independently.
"During our conversation I explained that there was an ongoing legal process involving FIFA's independent judicial bodies and that the case would be decided in due course by the competent bodies," Infantino said in a statement. "That is how FIFA's system works, and it is a principle that I will always uphold."
For UEFA, the decision to suspend the ban was wrong.
"We express our disbelief at such an unprecedented, incomprehensible and unjustifiable decision," UEFA said. "Yesterday's decision ... crossed a red line.
"When the certainty of rules is no longer guaranteed by its guardians, the integrity of the game is at stake and the credibility of a competition is undermined."
"The FIFA Appeal Committee has rendered a request submitted by the Royal Belgian Football Association (RBFA) as inadmissible," FIFA said in a statement. "The request was rendered inadmissible on the grounds that the RBFA is not a party to the proceedings and, as such, has no standing to appeal the decision."
In a further indication of politicians becoming involved the UK Prime Minister Keir Starmer said he intervened to ask FIFA not to bring forward kick-off at the Azteca for the Mexico-England match on Sunday (local time).
The change was suggested due to the risk of thunderstorms delaying the game (which they did, for an hour) but was feared to harm England's chances in a game they ultimately won 3-2.
Meanwhile, France have made an appeal asking FIFA to rescind the yellow card handed out to forward Michael Olise for a confrontation with Paraguay midfielder Matias Galarza on Saturday, The Athletic reported.