"No, I don't think so," the Maine independent said when asked on CNN's "State of the Union" whether Trump's claim was correct.
"It's certainly not commonly agreed in our committee, and we're the ones doing the investigation," he said, referring to his panel's investigation into Russia's efforts to influence the 2016 election. "I don't think there's any basis for that statement. It's entirely possible that we may end up in the investigation at the end that there wasn't, but the contrary could also be true."
On Friday, Trump tweeted, "It is now commonly agreed, after many months of COSTLY looking, that there was NO collusion between Russia and Trump. Was collusion with HC!"
King, whose panel is conducting one of several investigations into Russia's meddling in the election, said the committee will still be reviewing evidence for months, calling Trump's declaration "premature."
On Sunday morning, Trump took to Twitter again to slam the the Russia investigation, which is being led in the Justice Department by special counsel Robert Mueller, a former FBI director, as well as a related dossier of allegations against Trump that he has repeatedly said is not true.
As talk about the the first charges being filed in the Mueller investigation dominated the news Sunday, White House special counsel Ty Cobb said Trump's morning tweets about the Russia investigation were not related to the Justice Department special counsel's activities.
"Contrary to what many have suggested, the President's comments today are unrelated to the activities of the special counsel, with whom he continues to cooperate," Cobb told CNN, declining to comment further on the tweets.
In his interview Sunday with CNN's Jake Tapper, King added the news about charges being filed
in the Russia investigation, which CNN reported Friday, are "just the beginning."
"I think it's important to emphasize that whatever it is, it's just the beginning, and I'm sure there will be additional evidence, assuming Director Mueller uncovers additional evidence," he said.
King, who caucuses with Democrats in the Senate, also said he thought the timing of calls for Mueller to resign from the investigation and the news of indictments in that probe were probably not a coincidence.
"I don't see any reason why he should recuse himself or be fired," King said. "The fact that these charges are coming at kind of a crescendo at a very time there it appears they're also indictments, to be forthcoming, there is a kind of coincidence there that I don't think you can miss."