"We have a commander-in-chief and he has said he does not want war with Iran and the Saudi Arabians have said the same thing," Risch said on "The Story with Martha MacCallum" Wednesday.
"The unfortunate part of all of this is Iran continues to push the envelope."
U.S. Secretary of State Mike Pompeo on Wednesday doubled down on accusations Iran is responsible for the weekend bombing on Saudi Arabia’s oil facilities, telling reporters that the strike was “an act of war.”
Earlier, President Trump tweeted that he had ordered Treasury Secretary Steven Mnuchin to “substantially increase sanctions” on Iran.
Risch said the Iranians are "notorious for making bad judgments" and said that's what is happening with the current situation.
"[Trump] doesn't want war with Iran. Having said that sometimes you get pulled into something and have to do something that you don't necessarily want to do," Risch told MacCallum. "The Iranians are very very close to that."
The Foreign Relations Committee member also said it's hard to ignore the drone attacks.
"This was such a deliberate and overwhelming use of military force that it is very hard to look the other way," Risch said.
Fox News' Barnini Chakraborty contributed to this report.