The Democratic lawmakers addressed reporters on Capitol Hill one day before ousted FBI Director James Comey is expected to make bombshell revelations regarding Trump's attempts to interfere in the FBI's investigation into Russia's efforts to influence last year's presidential elections.
Green is the first lawmaker to publicly call for Trump's removal from office, and said he is doing so because Trump sought to obstruct justice.
"The president will not be indicted while he is in office, and while there is some merit in talking about the judicial process, the impeachment process is the one that will bring him before the bar of justice,” Green said.
The Texas Democrat, who is black, has faced a series of death threats rife with racial slurs after he announced in May that he would pursue impeachment.
Sherman acknowledged impeachment would not pass the House currently, but said it would be a process to muster the votes necessary to get it through.
During a separate news conference, Democratic congresswoman Linda Sanchez said "the overwhelming sentiment of" House Democrats is to wait for investigations to conclude.
"A majority of the caucus is of the belief that we ought to allow the investigation to continue to its logical conclusion before making any determination.," she said.
The FBI, House, and Senate are each conducting separate investigations into whether the Trump campaign and Russia colluded in last year's election.