The committee said it had approved subpoenas for Cohen and for Trump's former national security advisor Michael Flynn to appear before them and supply documents.
While Flynn has been a known target of congressional and Justice Department investigations into possible collusion between Moscow and the Trump presidential campaign, Cohen has only recently become a focus of the probe, for unknown reasons.
"As part of our ongoing investigation into Russian active measures during the 2016 campaign, today we approved subpoenas for several individuals for testimony, personal documents and business records," said Republican committee chair Mike Conaway and senior committee Democrat Adam Schiff.
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"We hope and expect that anyone called to testify or provide documents will comply with that request, so that we may gain all the information within the scope of our investigation. We will continue to pursue this investigation wherever the facts may lead."
Cohen spent years as the main lawyer for the Trump Organisation, the president's New York-based real estate and entertainment business.
Cohen was also mentioned as someone with Russian contacts in the still-unverified dossier on Trump campaign ties to Russia compiled by former British intelligence agent Christopher Steele.
Besides Cohen and Flynn, the investigations are believed to be examining Trump's son-in-law, Jared Kushner, former campaign chairman Paul Manafort, former political advisor Roger Stone, and erstwhile foreign policy consultant Carter Page.
The House and Senate Intelligence Committees continue to press ahead in their investigations, even as a newly-appointed independent special counsel takes over the Justice Department and FBI investigations into possible collusion between the Trump campaign and Russia.
The special counsel, former Federal Bureau of Investigation director Robert Mueller, was appointed two weeks ago amid worries over Trump's possible interference in the probe.
