Rep. Jackie Speier, a California Democrat on the committee, told CNN Nunes tried to set the record straight Thursday morning.
Rep. Elijah Cummings, however, told the network he would like to see Nunes investigated for his actions.
"Basically what he has done is he has scuttled and put a cloud over his own investigation and he has become the subject — he should be — of an investigation," the Maryland Democrat said. "It's a real problem.
"What he did was basically to go to the president, who is being investigated by the FBI and others and by the intelligence committee, to give them information."
Speier told reporters on Capitol Hill Thursday there are serious questions about Nunes's future on the committee.
"He knows, full well, that there is grave question about his objectivity and I think over the next few days we are going to assess whether or not we feel confident that he can continue in that role," she said, according to Reuters.
Nunes' comments this week came after FBI Director James Comey said there is no evidence to suggest Trump Tower was the subject of surveillance before and after the presidential election, refuting Trump's claim otherwise.