Schiff said it "deeply concerns me that the president would make such an accusation without basis."
The committee's chairman, Rep. Devin Nunes, R-Calif., said, "I don't think there was an actual tap of Trump Tower."
Trump alleged in a series of tweets that Obama had his phones tapped.
"The challenge here is that the President Obama wouldn't physically go over and wiretap and then you have to decide if you're going to take the tweets literally, and if you are, then clearly the president was wrong." Nunes said referring to the multiple tweets that Trump sent on the morning of March 4.
"But if you're not going to take the tweets literally and if there's a concern that the president has about other people, other surveillance activities looking at him or his associates, either appropriately or inappropriately, we want to find that out. It's all in the interpretation of what you believe," he said.
White House press secretary Sean Spicer maintained that Trump will be "vindicated" by evidence. On March 13, Spicer said that Trump was not talking literally or specifically when he accused Obama of "wiretapping" his campaign.
"If you look at the president's tweet, he said 'wiretapping' in quotes. There's been substantial discussion in several reports," Spicer said.
"The president was very clear in his tweet. It was wiretapping. That spans a host of surveillance options," he said. "The House and the Senate Intelligence committees will now look into that and provide a report back. I think there's been numerous reports from a variety of outlets over the last couple months that seem to indicate that there has been different types of surveillance that occurred during the 2016 election."
Nunes said that there will be a public hearing about the issue in the coming weeks. Schiff said committee members will ask Justice Department officials whether they have seen "any evidence that substantiates the president's claim."