Mr Trump disputed in another interview aired this week whether the FBI should be notified of such approaches.
What did President Trump tell Fox?
On Friday, Mr Trump called into the Fox & Friends show to give a 50-minute live interview.
Asked how he would respond to any offer from another government to help his campaign, Mr Trump said: “Of course, you give it to the FBI or report it to the attorney general or somebody like that.”
He continued: “But of course you do that. You couldn’t have that happen with our country.”
Mr Trump also maintained he would still at least review any such foreign-supplied information.
“Of course, you have to look at it, because if you don’t look at it, you won’t know it’s bad,” he said.
What did he say earlier this week?
In an interview broadcast this week on ABC News, Mr Trump pushed back on whether he should report to law enforcement officials any foreign offer of help for his re-election bid.
Mr Trump said: “If somebody called from a country, Norway, ‘we have information on your opponent’ – oh, I think I’d want to hear it.”
“It’s not an interference, they have information,” Mr Trump added, “I think I’d take it.”
“If I thought there was something wrong, I’d go maybe to the FBI – if I thought there was something wrong.”
When the ABC anchor referred to the FBI director telling Congress his agency should be made aware of any such foreign election meddling, Mr Trump said: “The FBI director is wrong.”
What was the reaction?
Even several of the president’s fellow Republicans spoke out against his remarks to ABC.
Trump ally Senator Lindsey Graham said the comments were “wrong”.
Democratic Speaker of the House Nancy Pelosi said the president “does not know right from wrong”.
And in a pointed tweet, Federal Election Commission chairwoman Ellen Weintraub clarified the rules.
What else did Trump tell Fox?
The Office of Special Counsel said Mrs Conway’s disparaging comments about Democratic candidates were banned political activities under the Hatch Act.
But Mr Trump told Fox & Friends: “No, I’m not going to fire her. I think she’s a terrific person.
“I think you’re entitled to free speech in this country.”