House Republican leader Kevin McCarthy of California received bipartisan support for his motion to table the resolution. The chamber voted 332-94, with 137 Democrats joining their Republican colleagues in support.
Green, D-Texas, advanced the resolution for a vote with a procedural move Tuesday night, when he read it on the House floor.
"Donald John Trump, president of the United States, is unfit to be president, unfit to represent the American values of decency and morality, respectability and civility, honesty and propriety, reputability and integrity," he said.
Green's resolution came after the House voted to condemn Trump's tweets against four members of Congress, telling them to "go back and help fix the totally broken crime infested places from which they came." That resolution "strongly" condemned Trump's "racist comments that have legitimized and increased fear and hatred of new Americans and people of color," and passed by a vote of 240-187. Four Republicans voted in favor.
"To condemn a racist president is not enough, we must impeach him," Green added. "This will be a defining vote. The world is watching, and history will judge us all."
The House is also set to vote on holding U.S. Attorney General William Barr and Commerce Secretary Wilbur Ross in criminal contempt of Congress for withholding information about the Trump administration's effort to add a citizenship question to the 2020 Census.
Calls for Trump's impeachment among Democratic lawmakers have grown since special counsel Robert Mueller's report was made public in April. It listed 10 occasions in which the president may have obstructed justice by attempting to disrupt the Russia investigation.
A slight majority of Americans do not favor impeaching Trump. A Gallup survey this month said 53 percent of respondents were opposed the idea.
House Speaker Nancy Pelosi could sway members to table Green's impeachment motion, or delay it in the Judiciary Committee. Green said he would fight any move to shelve a vote.