Secretary of State Marco Rubio indicated last week the Trump administration had "no problem" with providing visas to Iran's team.
High temperatures could be in place in several of the host cities during the World Cup.
FIFA has made a late change of policy to bar World Cup fans from bringing refillable water bottles into the tournament's 16 stadiums across North America.
Officials say the investigation will probe a range of issues, including FIFA's ticketing process.
U.S. hotels say the promised economic boon from the World Cup hasn't materialized yet for them.