Baghdad, Iraq ? The United States soon will trim its military force in Iraq to slightly below 138,000 troops, the level it has considered its core force this year, Defense Secretary Donald H. Rumsfeld and other U.S. officials hinted Thursday.

The cuts, probably in the 5,000 to 7,000 range, would be achieved by canceling the planned deployment to Iraq of two Army brigades and could be announced as early as today, officials said.

The reduction would bring the troop level in the insurgency-torn country to just above 130,000 sometime in the spring, said one U.S. Defense Department official who spoke on condition of anonymity because an announcement was not yet finalized.

President Bush is under growing pressure from two fronts to pare back the American force in Iraq: the Republican-run Congress and a public increasingly disenchanted with the war and its growing casualties, which have surpassed 2,100 U.S. war dead and 15,000 wounded.

The president, Rumsfeld and other Bush administration and military officials long have said that U.S. troop reductions would occur as the Iraqis show signs of being able to take control of their country. As evidence of progress, these officials in recent weeks have pointed to growing numbers of Iraqi troops they say are capable of lead combat roles.

The reductions discussed Thursday would come in addition to Rumsfeld’s previous announcement that about 20,000 troops are to return home after bolstering security during Iraq’s fall elections.

U.S. Secretary of Defense Donald H. Rumsfeld, left, meets troops at the Al Faw Palace in Baghdad, Iraq. Rumsfeld arrived unannounced Thursday in Baghdad to hold talks with U.S. commanders and assess the next phase of U.S. troop deployments in Iraq.

There were 159,000 U.S. troops in Iraq on Thursday. The American force peaked at 192,000 during the March 2003 invasion; the monthly low was 109,000 in January 2004.

Rumsfeld, on an unannounced trip to Iraq, was asked by reporters whether he had decided to hold back the deployment of the 1st Brigade of the 1st Infantry Division from Fort Riley, Kan., and the 2nd Brigade of the 1st Armored Division, now in Kuwait.

Other officials have said those brigades’ planned deployments would be canceled, with small parts of each brigade probably going to help train Iraqis.

Rumsfeld would not answer directly, but hinted that an internal decision had been made.

“Until it’s announced, the government’s decision hasn’t been announced. Therefore it’s not final,” he said.

Upon his arrival in the Iraqi capital, Rumsfeld met with Gen. George Casey, the top U.S. commander in Iraq, and Zalmay Khalilzad, the U.S. ambassador to Baghdad.

Pressed later to explain the rationale for canceling the two brigades’ deployments, Casey said, “Not until it’s announced – if it’s announced.”

At the Pentagon, Lt. Gen. James T. Conway, director of operations for the Joint Chiefs of Staff, said the 1st Infantry Division is expecting further orders.

“We owe … the 1st Infantry Division another order, if you will, to somehow change their status,” he said. “And that will happen some time, I think, before the end of the year.”

It was Rumsfeld’s 11th trip to Iraq since the war began.