The broad requests from the House intelligence, Foreign Affairs and Oversight and Reform committees ask for the substance of Trump and Putin's conversations in person and by phone and for information on whether those conversations had any impact on USA foreign policy.
The New York Democrat has repeatedly expressed his view in recent months that Trump either clearly obstructed justice, or attempted doing so, by seeking to curtail special counsel Robert Mueller's investigation into possible Trump campaign collusion with Russian Federation during the 2016 presidential election.
"We are going to initiate investigations into abuses of power, into corruption and into obstruction of justice", Mr Nadler said.
"Congress must provide a check on abuses of power", he said. "The (White House) Counsel's Office and relevant White House officials will review it and respond at the appropriate time".
That meeting included Trump Jr., Kushner, Trump's former campaign manager Paul Manafort and Russian lawyer Natalia Veselnitskaya, who had "dirt" to offer about Democratic presidential nominee Hillary Clinton, according to an email made public.
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At the White House, Trump was asked if he would cooperate with Nadler's probe.
Among the committee's aims is determining whether Trump obstructed justice by ousting perceived enemies at the Justice Department, such as former FBI Director James Comey, and abused his presidential power by possibly offering pardons or tampering with witnesses.
Trump fueled suspicions a year ago about his ties with Russian Federation when, in a sharp break with standard diplomatic practice, he dismissed top aides for two hours of talks with Putin during their first formal summit, in Helsinki.
Included in the requests were the Trump Organization, as well as several employees invoked by former Trump attorney Michael Cohen during his hearing last week before the House oversight committee: Chief Financial Official Allen Weisselberg, Executive Vice President Matthew Calamari, and President Trump's longtime personal assistant Rhona Graff.
The three chairmen on Monday cited reports that Trump "seized notes pertaining to at least one meeting he held with President Putin" and directed an interpreter to not discuss with other USA officials the substance of the communications.
A counsel for the House Judiciary Committee said in a phone call with reporters on Monday that document requests have been sent to 81 people and organisations. "He tried to protect Flynn from being investigated by the Federal Bureau of Investigation". The President's two sons, Eric Trump and Donald Trump Jr., also received requests, as did the White House and his son-in-law, Jared Kushner.