In a letter late on Tuesday to House Speaker Nancy Pelosi, Pence said the mechanism should not be used "as a means of punishment or usurpation" and reserved for cases of medical or mental incapacitation.
Pelosi has called on Pence to secure the majority of the cabinet and vote to declare Trump unfit to serve.
As the House appears on the cusp of a bipartisan impeachment of Trump, Pence encouraged Congress to avoid actions to "further divide and inflame the passions of the moment" and to focus on smoothing the transition to President-elect Joe Biden's administration.
Pelosi has said if Pence rejects use of the 25th Amendment, the House will move to impeach him.
Already, at least three Republicans have said they would vote for that.
Liz Cheney, the No.3 Republican in the House of Representatives, said: "There has never been a greater betrayal by a president of the United States of his office and his oath to the Constitution."
Trump "summoned this mob, assembled the mob and lit the flame of this attack" on the Capitol last Wednesday, Cheney, the daughter of former Republican vice-president Dick Cheney, said in a statement, adding: "I will vote to impeach the president."
Two other Republican House members, John Katko and Adam Kinzinger, said they would also vote for the historic second impeachment of the Republican president, who leaves office in just eight days.