WASHINGTON, July 31 — Leading Congressional Democrats, after months of division over Iraq, have called on President Bush to begin a phased redeployment of troops by the end of this year, a unified statement signaling they have concluded that the war could hurt Republicans in the midterm elections.

The letter called on American forces in Iraq to make a transition to a “more limited mission” dealing with counterterrorism and training and logistical support of Iraq security forces.

“In the interests of American national security, our troops, and our taxpayers, the open-ended commitment in Iraq that you have embraced cannot and should not be sustained,” said the letter, dated July 30 and released Monday. It was signed by a dozen Democratic leaders, including Harry Reid of Nevada, the Senate minority leader, and Nancy Pelosi, the House Democratic leader.

“Mr. President, simply staying the course in Iraq is not working,” the Democrats wrote. “We need to take a new direction. We believe these recommendations comprise an effective alternative to the current open-ended commitment, which is not producing the progress in Iraq we would all like to see.”