The statement came amid an increasingly bitter standoff over Infantino's leadership following the collapse of his proposal to raise about $4.2 billion by selling a stake in the commercial rights of the World Cup and other tournaments.
The plan triggered criticism from UEFA, national associations and senior FIFA officials, led to calls for Infantino to resign and prompted a crisis meeting in Morocco this week at which FIFA's leadership reaffirmed its support for the president.
FIFA did not identify those it said were seeking to undermine Infantino or specify which reports or allegations it was referring to.
The statement followed reports by The Daily Telegraph about payments made by UEFA to a former employee during Infantino's time as the European governing body's general secretary, allegations he has denied and that FIFA has rejected as unfounded.
"Those who do not have the support of FIFA's Member Associations should not seek to achieve through allegation, insinuation or misinformation what they cannot achieve through FIFA's established democratic processes," FIFA said.
It said recent reporting had included "unsubstantiated assertions and demonstrably false claims" concerning FIFA and its president, adding that it would challenge inaccurate or misleading reports "directly and vigorously".
FIFA added it would not support, facilitate or tolerate any process concerning the election of its president that was inconsistent with its statutes, democratic procedures and governance framework.
"The FIFA president was democratically elected by FIFA's member associations and continues to serve with their mandate," it said.
Splits supported
Following a crisis meeting in Morocco on Wednesday, FIFA apologised to its 211 member associations for mistakes in the handling of the proposal and said its leadership had reaffirmed its full support for Infantino.
The fallout has cast a shadow over Infantino's bid for a fourth term at the FIFA Congress in Morocco in March. No clear candidate to challenge him has yet emerged.
UEFA has said it no longer has confidence in Infantino, while Norwegian Football Federation President Lise Klaveness called for him to resign on Friday, saying he no longer had the institutional trust required to govern FIFA.
But Infantino continues to enjoy substantial support among FIFA's 211 members. The Confederation of African Football (CAF) unanimously backed his leadership on Thursday, while South America's CONMEBOL rejected any attempt to oust him that did not involve a vote of all FIFA members.
Mexico's football federation (FMF) also backed Infantino, despite its regional confederation CONCACAF having called for a "comprehensive reckoning" with his presidency.
"The FMF will neither recognise nor approve any process convened outside of that institutional framework," the Mexican federation said.