The committee has ordered lawyer Michael Cohen and security adviser Michael Flynn to appear before them and supply documents. "We will continue to pursue this investigation wherever the facts may lead", Rep. K. Michael Conaway (R-Texas), the committee chairman, and Rep. Adam B. Schiff (D-Burbank), the ranking member, said in a statement.
The committee also issued subpoenas to former National Security Advisor Michael Flynn, who resigned under pressure after failing to disclose meetings with Russian officials, as well as businesses owned by the two men.
Four of the seven subpoenas were related to the committee's investigation into Russian interference in the election, according to The Wall Street Journal.
Cohen told ABC on Tuesday that he "declined the invitation to participate, as the request was poorly phrased, overly broad, and not capable of being answered".
Three others concern questions about how and why the names of Trump associates were unredacted and distributed within classified reports by Obama administration officials during the presidential transition. Flynn previously invoked his Fifth Amendment protection against self-incrimination.
Nunes' role in the issuing of subpoenas has been a sore point behind the scenes in the House investigation ever since he announced he was recusing himself from leading the Russian Federation investigation.
Flynn was forced to resign when it was reported in February that he had spoken to the Russian ambassador about U.S. sanctions and then misled Vice President Mike Pence about his contacts.
Three of the subpoenas were directed to the CIA, FBI, and NSA over the unmasking claims.
The Trump-Russia investigations, both in relevant congressional committees and within the FBI, have picked up steam over the last few weeks, following Trump's decision to abruptly fire FBI Director James Comey.
The Senate intelligence committee announced Comey's appearance, and a Comey associate said he had been cleared to testify by Robert Mueller, another former FBI director now overseeing that investigation as special counsel.
Nunes, who was a member of Trump's transition team, had raised the topic of unmasking - the practice of identifying by name individuals mentioned in surveillance transcripts - after the committee heard testimony March 20 from then Federal Bureau of Investigation director James Comey that the FBI was investigating possible collusion between the Trump campaign and Russian Federation during last year's election campaign.
The committee's announcement doesn't detail whether the subpoenas to Flynn and Cohen contain specific deadlines. Instead, Nunes said he'd been shown documents that he said suggested the Obama administration had acted improperly in "unmasking" the names of Trump associates monitored communicating with foreign officials.
These subpoenas are seeking records related to the "unmasking" of Trump associates accidentally picked up in intercepted conversations, say United States media reports.
A separate congressional source confirms that Nunes separately issued the other subpoenas, not Conaway and Schiff, who are leading the Russian Federation investigation.