"I could argue the mayor started it months ago," Rep. Chris Collins, R-New York, told CNN's Alisyn Camerota on "New Day" Tuesday. "Let's just say they are not friends. They are, you know, adversaries to the standpoint of jabbing at each other."
"One thing we know about President Trump is he does jab back," Collins added.
Donald Trump Jr. also came to his father's defense Tuesday morning, saying despite the criticism, his father's tweets are right, casting blame on Khan.
"Every time he (President Trump) puts something out there, he gets criticized by the media all day every day and by everyone else, and guess what, two weeks later he's proven to be right. (Terrorism) happened again and we keep appeasing it and we keep saying OK, it's going to be great," Trump Jr. said in an interview with ABC News.
The President's eldest son criticized Khan for "attacking" his father, even though President Trump initiated the tweets.
"This is a recurring theme and we're attacked but rather than the mayor of London attacking, maybe he should do something about it. Maybe he should do something to fix the problem rather than just sit there and pretend there isn't one," he said.
Asked whether he believes Khan is at fault for what happened, Trump said, "I'm not. No. That's not what I said. I think it's time for people to act and do something more proactive than what's going on and that's what people have to do. We can't just sit there and pretend it's not a problem."
Trump said that rather than keep calm and carry on, "maybe we have to keep calm and do something" in the wake of terrorist attacks.
The feud between the two leaders stretches back as far as Trump's proposed "Muslim ban" as a candidate, though it was revived in the aftermath of the London attack when Khan said there was "no cause for alarm" in reference to a visible increase in police activity on the streets of London.
But Trump appeared to misconstrue the statement on Sunday when he tweeted: "At least 7 dead and 48 wounded in terror attack and Mayor of London says there is "no reason to be alarmed!"
Although Trump was criticized for attacking Khan, he continued his criticism Monday.
"Pathetic excuse by London Mayor Sadiq Khan who had to think fast on his 'no reason to be alarmed' statement. (Mainstream media) is working hard to sell it!" Trump said.
Khan responded Monday by saying a planned state visit by Trump to the UK should be called off.
"I don't think we should roll out the red carpet to the President of the USA in the circumstances where his policies go against everything we stand for," Khan told the UK's Channel 4 News.
"When you have a special relationship it is no different from when you have got a close mate," he added. "You stand with them in times of adversity, but you call them out when they are wrong. And there are many things about which Donald Trump is wrong."