House Judiciary Committee Chairman Jerrold Nadler told CNN that nobody should draw conclusions just because some people affiliated with Trump's administration and businesses were not included on the initial list.
"Investigating these threats to the rule of law is an obligation of Congress and a core function of the House Judiciary Committee", he said.
Nadler said Sunday he believes the president has obstructed justice. One of the most intriguing of these lines of inquiries led to a letter sent Monday by the chairs of the Intelligence, Oversight, and Foreign Affairs committees: what exactly is the nature of Trump's communications with Russian President Vladimir Putin?
FILE - Special counsel Robert Mueller, in charge of investigating Russian interference in the 2016 US presidential election and possible collusion between Moscow and the Trump campaign, departs Capitol Hill, in Washington, June 21, 2017.
Trump dismissed the Nadler probe and others as futile efforts "in search of a crime".
Trump told reporters after Nadler's probe was announced that "I cooperate all the time with everybody".
The information gathered by the Judiciary Committee, along with that in the yet-to-be-released report by special counsel Robert Mueller's investigation of Trump campaign links to Russian Federation and obstruction allegations, could form the basis of impeachment proceedings against Trump.
Trump rips into Mueller probe at CPAC during lengthy speech
He also railed against special counsel Mueller's investigation and attacked Democrats as socialists. In the other way, I love Mr. and Mrs.
The letters submitted by the New York Democrat were sent to many in Trump's inner circle, including his sons Donald Trump Jr. and Eric Trump, former White House and 2016 presidential campaign aides as well as people involved with the Trump Organization, among them Chief Financial Officer Allen Weisselberg. White House Press Secretary Sarah Sanders said Monday the White House had received the letter and that "the counsel's office and relevant White House officials will review it and respond at the appropriate time".
Republicans in Congress said that Democrats are pursuing an impeachment agenda against Trump as part of a political strategy to reclaim the White House in the 2020 election.
In addition to focusing on obstruction allegations, the committee said it is looking at possible public corruption and abuses of power during the two-year Trump presidency.
Democrats secured the majority in the House of Representatives in the 2018 midterm election, and with it, the power to launch investigations.
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. Several other committees are probing related matters as well, and while many might overlap, the committee chairmen and chairwomen say they are working together on the investigations.
There are also people connected to Russian interference in the 2016 campaign, including participants in a meeting at Trump Tower with a Russian lawyer before the election.
The committee seeks from Cohen, Trump's former personal lawyer who called Trump a "con man" and a "cheat" in congressional testimony last week, "any audio or video recordings" of conversations with Trump or conversations about his presidential campaign. 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".