The race at Austin's Circuit of the Americas (COTA) is scheduled for November 2, the same day the NASCAR Sprint Cup's AAA Texas 500 takes place at the Texas Motor Speedway in Fort Worth, leading to criticism from Eddie Gossage, the president of Texas Motor Speedway.
He said: "I think it's foolish. Nobody wins. It's a shot fired by Formula One at NASCAR. I can't say I was surprised because Bernie Ecclestone does a lot of foolish things.
"The thing he unfortunately doesn't recognise is there is an 800lb gorilla when it comes to major American motor sports. The 800lb gorilla is NASCAR."
Gossage added: "It's just not smart. There are 52 weeks in the year. But that was the only weekend Formula One could make it work in Austin, Texas? Give me a break.
"It wouldn't have happened if [the COTA officials] had the strength and the fortitude to stand up and say no."
Ecclestone, however, feels Gossage lacks appreciation of not only the logistics of F1, but also the differing markets of the two sports.
He said: "We've a small problem they [NASCAR] don't have - we have six jumbo jets to move our equipment around and we have to find the most sensible way to use them to do that.
"We have to be efficient, and bear in mind we may also encounter problems at an airport. There are issues that can occur, but he and other people do not realise these things.
"The race prior to the one in the US is in Russia, in Sochi. We've never been before, and we have to get out of there and into Austin.
"That is probably a lot easier than trying to get into Brazil, and then we have to get out of there to go to Abu Dhabi. He is very lucky he doesn't have to do what we have to do."
Ecclestone appreciates some fans might want to attend both events, but believes they are a minority.
"I've spoken to the people who run the race at COTA and they believe the NASCAR crowd is a different crowd from the Formula One crowd, different people, different customers," the 83-year-old said.
"At the end of the day they run a domestic series in America - we run a world championship."