The investigation was subsequently taken over by Special Counsel Robert Mueller, who is expected to end his investigation and report his findings to Attorney General William Barr in coming weeks.
The House Intelligence, Foreign Affairs and Government Oversight committees say they wrote to acting White House Chief of Staff Mick Mulvaney and Secretary of State Mike Pompeo seeking documents and interviews on Trump's communications with Putin.
And past year, the White House announced that it would stop the practice of regularly issuing readouts of phone calls between Trump and foreign leaders, which means the public has no idea how often he speaks with Putin by phone.
Nadler said Mueller and prosecutors conducting investigators in the Manhattan US Attorney's Office are aware of the committee's action.
Republicans in congress accuse Democrats of pursuing an impeachment agenda as part of a political strategy to reclaim the White House in the 2020 election.
Trump implied on Monday that he would work with the panel: "I cooperate all the time with everybody", he told a reporter who asked whether he would help Nadler.
Comey was leading an investigation into Russian activities in the 2016 USA presidential election and possible collusion with Trump's campaign when the president fired him in May 2017.
Nadler went on to say that numerous president's public statements added up to obstruction, but that they needed more evidence to act on that accusation. The Oversight and Reform Committee has launched multiple investigations into all facets of the administration.
They include former Trump national security adviser Michael Flynn, former campaign chairman Paul Manafort, former Trump adviser Roger Stone and Cohen.
Also on the committee's list are others who worked on Trump's 2016 campaign or in the White House such as Hope Hicks, Steve Bannon, Reince Priebus and Sean Spicer; Rhona Graff, a long-time executive assistant at the Trump Organization; and David Pecker, chief executive of American Media, which publishes the supermarket tabloid National Enquirer.
The probe will try to ascertain, among other things, whether Trump obstructed justice by removing perceived enemies in the Justice Department such as ex-FBI Director James Comey.
Trump and Putin met privately in Helsinki in July for more than two hours with only interpreters present. He emerged empty-handed from a high-profile summit with North Korean leader Kim Jong Un on denuclearisation, and Mr Trump's former personal lawyer Michael Cohen, in three days of congressional evidence, publicly characterised the president as a "conman" and "cheat".
In a tweet on Sunday, Trump blasted Mueller's Russian Federation investigation, calling it a partisan probe unfairly aimed at discrediting his win in the 2016 presidential election.
"We're far from making decisions" regarding impeachment, Nadler said Sunday. They said they intend to probe "the substance of any communications during in-person encounters and phone calls, the existence and contents of any documents related to the communications, what the effects of the communications have been on the nation's foreign policy, whether the president or anyone acting on his behalf have sought to hide those communications and whether the president or anyone acting on his behalf have failed to create records or mishandled those records in violation of federal law".