The House Judiciary Committee approved the resolution for the probe, despite doubts about the viability of an impeachment as the Republican-controlled Senate is unlikely to vote to strip Trump of his presidency should the entire House vote to impeach him.
Party leaders like Speaker Nancy Pelosi have been hesitant to proceed with impeachment, because of the likely Senate roadblock and the distraction it could cause during the election year.
But a majority of Democrat Representatives - 134 out of 235 - have gone on record demanding impeachment proceedings, and if it comes to a vote before the entire 435-member House, other Democrats would join them to pass it.
Foremost among those calling for impeachment is Pramila Jayapal, who belongs to the party's progressive wing. Raja Krishnamoorthi and Ro Khanna also support impeachment.
Judicial Committee Chairman Jerry Nadler's tactic bypasses a vote by the entire House to authorise impeachment proceedings, which Republicans say is necessary, by calling it an investigation rather than a formal impeachment.
A judgement by Federal Judge Amit Mehta bolsters Nadler's position. He ruled in May that Congress can demand evidence of alleged illegal behaviour by a President even if there is no formal impeachment proceedings.
The resolution allows committee members and staffer to extensively question witnesses and also to hold hearings before the full committee or spread them around subcommittees, laying the groundwork for formal impeachment proceeding, should the House approve it.
The Republican leader in the committee, Doug Collins, said the Democrats were trying to "to make it appear that something is happening that is not".
The impeachment issue is likely to figure in the Democratic Party's presidential debate of candidates vying for the party's nomination to run against Trump in next year's election.
Nadler said the Committee's measure was a necessary "next step" and the investigation "will allow us to determine whether to recommend articles of impeachment".
Articles of impeachment are like a charge sheet, laying out the grounds for the removal of a President that the Senate must approve.
The main charges that the committee is expected to consider are if Trump tried to obstruct justice by interfering with the probe into alleged links to Russian election meddling and if he used his office to make his businesses profit.
Special Counsel Robert Mueller, who investigated the allegations did not find that he colluded with Russ, but did not make a conclusive finding on obstruction of justice.
(Arul Louis can be contacted at arul.l@.in and followed on Twitter @arulouis)
( With inputs from IANS )