Texas Democrat Al Green filed the resolution after the House voted to denounce Mr Trump's attacks aimed at four US congresswomen as racist.
But the measure failed to win enough support, with his fellow Democrats voting overwhelmingly against.
Mr Trump said the "ridiculous" attempts to impeach him were now "over".
"This should never be allowed to happen to another President of the United States again!" he tweeted.
This week's attempt came on the heels of Mr Trump's repeated attacks against four congresswomen, which began with a series of tweets telling the unnamed politicians to "go back" to their countries.
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