Rep. Trey Gowdy admonished the White House on Sunday for extending an invitation for Russian President Vladimir Putin to visit the U.S. in the fall.

"Those should be reserved, I think, for our allies like Great Britain, and Canada, and Australia, and those who are with us day in and day out," Gowdy, R-S.C., said on "Fox News Sunday. "I think we should be very judicious in who we invite and place that in imprimatur of acceptance on — so I hope the president would keep that in mind if we are issuing invitations to foreign leaders."

[Opinion: Trump-Putin the sequel would be worse than the original]

While Gowdy said it is important for the president to meet with foreign leaders who aren't close allies, he said explicitly,"Russia is not our friend," and advised Trump to be wary in dealing with them.

Trump met with Putin in Helsinki last week, and was widely criticized for meeting with the Russian leader in private for two hours and for comments he made during a joint press conference, in which he cast aside U.S. intelligence and said he had no reason to not believe Putin when he said the Russian government was not involved in interference in the U.S.'s 2016 election. Further adding to his critics' furor, Deputy Attorney General Rod Rosenstein announced right before the meeting in Finland that special counsel Robert Mueller had indicted 12 Russian officials on charges of hacking Democrats' computers during the 2016 campaign.

Amid backlash, Trump has since walked back those comments, saying he holds Putin "responsible" for meddling in the U.S. electoral process.

Gowdy called Putin being invited to the White House without Director of National Intelligence Dan Coats knowing about it ahead of time "strange."

Coats appeared to be caught off guard at the Aspen Security Forum in Colorado on Thursday when he was informed of a White House tweet that said a Putin visit was being discussed for the fall. After asking for the news to be repeated, Coats said with a chuckle: "OK. That’s going to be special.”

When asked about Coats' apparent surprise on "Fox News Sunday," Gowdy, R-S.C., said, "I do think it was strange."