President Donald Trump supports continuing daily U.S. military strikes on Iran, Sen. John Kennedy told CBS News' "Face the Nation" on Sunday, arguing that the United States should maintain pressure on Tehran through sustained military action and an ongoing blockade.

The Louisiana Republican said the recent pause in strikes this weekend should not signal a broader change in strategy.

"I think we ought to tighten the sanctions on the sale of Iranian oil. I think we ought to continue the blockade and starve them out," the senator said. "I think we ought to bomb Pickaxe Mountain and try to reach what's underneath it. ... The president likes the daily attacks."

Kennedy said Trump "believes that sometimes you have to kill a few chickens to scare the monkeys."

The senator described Iran's leadership as irrational, comparing its rulers to serial killer David Berkowitz, the "Son of Sam," and cult leader Charles Manson.

"They're more than mildly insane," Kennedy said, arguing the United States should not abandon its campaign despite the costs.

"I don't think we ought to just cut and run. If we can stand the pain of the rising cost of energy, we need to stay the course," he said. "At least for a few more months. I also don't think we need to send in troops."