Iran’s soccer team would be allowed to enter the United States to play in the World Cup this summer, but the Trump administration would deny entry to Iranians with ties to the country’s military, Secretary of State Marco Rubio said on Thursday.

The United States is co-hosting the 48-team World Cup this year with Canada and Mexico, starting June 11. The Iranian team qualified for the tournament last year but its participation was thrown into considerable doubt after the United States and Israel launched their war against Iran in February.

During an event at the White House on Thursday, Mr. Rubio and President Trump both suggested that Iranian soccer players coming to the United States for the tournament would be welcome.

“Nothing from the U.S. has told them they can’t come,” Mr. Rubio told reporters. “If they decide not to come on their own, it’s because they decided not to come.”

But Mr. Rubio said that anyone with ties to Iran’s Islamic Revolutionary Guards Corps would not be allowed in.

“What they can’t bring is a bunch of I.R.G.C. terrorists into our country and pretend that they are journalists and athletic trainers,” he said.

“We would not want to affect the athletes,” Mr. Trump quickly added.

American and Iranian officials have given mixed signals about Iran’s participation in the World Cup.

Mr. Trump said in March that he did not care if the Iranian team played in the World Cup. Later that month, he said that while Iran’s players would be welcome, it would not be appropriate for them to come to the United States “for their own life and safety.”

Iran’s sports minister said last month that the national team could not countenance taking part in the World Cup after the country’s supreme leader, Ayatollah Ali Khamenei, was killed in U.S.-Israeli strikes. This week, an Iranian government spokesman told state media that the team was preparing to play its World Cup matches in the United States.

Gianni Infantino, the head of soccer’s global governing body, FIFA, said last week that Iran was “coming for sure” to the World Cup.

“We hope that by then, of course, the situation will be a peaceful situation,” he said, speaking at a CNBC event in Washington. “As I said, that would definitely help. But Iran has to come, of course, they represent their people. They have qualified. The players want to play.”

All three of Iran’s group stage matches are in the United States — two in Los Angeles and the third in Seattle.

Mr. Trump and Mr. Rubio made their comments about the World Cup after a reporter asked what the president thought about Italy replacing Iran in the tournament. The Financial Times had reported that Paolo Zampolli, a U.S. special envoy and a close friend of the president’s, had proposed the switch to Mr. Trump and Mr. Infantino.

“I don’t think about it too much,” Mr. Trump said.

Italy’s sports minister, Andrea Abodi, and some fans have dismissed the idea.