FALLUJAH, Iraq (AP) – Just days after Iraq’s elections, Defense Secretary Donald H. Rumsfeld on Friday announced the first of what is likely to be a series of U.S. combat troop drawdowns in Iraq in 2006.

Rumsfeld, addressing U.S. troops at this former insurgent stronghold, said President Bush has authorized new cuts below the 138,000 level that has prevailed for most of this year.

Rumsfeld did not reveal the exact size of the troop cut, but Pentagon officials have said it could be as much as 7,000 combat troops. The Pentagon has not announced a timetable for troop reductions, but indications are that the force could be cut significantly by the end of 2006.

That could include substantial reductions well before the November midterm congressional elections, in which Bush’s war policies seem certain to be a major issue.

Rumsfeld said two Army brigades that had been scheduled for combat tours — one from Fort Riley, Kan., the other now in Kuwait — would no longer deploy to Iraq. That would reduce the number of combat brigades in Iraq from 17 to 15.

“The effect of these adjustments will reduce forces in Iraq by the spring of 2006 below the current high of 160,000 during the (Iraqi) election period to below the 138,000 baseline that had existed before the most recent elections,” the defense secretary said.

Rumsfeld aides said details were to be provided later at the Pentagon.

Further reductions will be considered “at some point in 2006,” after the new Iraqi government is in place and is prepared to discuss the future U.S. military presence, Rumsfeld added.

The Pentagon sent an extra 20,000 troops to Iraq to bolster security during the recent elections, and Rumsfeld has previously said those 20,000 would be withdrawn in January to return U.S. force levels to a 138,000 baseline.

Friday’s announcement marks the first time Rumsfeld has said troop levels will dip below that baseline.

Rumsfeld has said repeatedly that troop reductions depend on political progress in Iraq and improvements in Iraq’s own security forces. Later, the defense secretary flew to Amman to visit a military training center outside the Jordanian capital where a small number of Iraqis are trained in commando skills.

He watched Jordanian special operations soldiers in a mock assault on a building, using live ammunition, and then spoke to a group who are among the 92 undergoing training now. Rumsfeld told them their work is important to eventually allowing U.S. troops to leave their country.

“The United States and the coalition countries are anxious to turn over the security responsibilities to the Iraqis as soon as we are able to do so,” said Rumsfeld, who arrived in the country Thursday for his 11th visit since the U.S.-led invasion in March 2003.

Bush is under growing pressure from the Republican-run Congress to cut U.S. forces in Iraq. The conflict’s acceptance by American voters has plummeted as the war’s toll has mounted to more than 2,100 U.S. war dead and 15,000 wounded.

Bush, Rumsfeld and other administration officials have said a withdrawal would begin when the U.S.-trained Iraqi security forces show sufficient signs of being able to defend the country against insurgents.

There were 159,000 U.S. troops in Iraq on Thursday.

Iraq on Oct. 15 held a constitutional referendum, and on Dec. 15 held elections for a full-term government.

For the first time since the insurgency took hold in Iraq in midsummer 2003, Rumsfeld was spending the night in the country. He previously had made Iraq day trips but spent the night in other countries in the region.

In Afghanistan earlier Thursday, military officials said they were progressing toward eliminating the Taliban resistance and al-Qaida terrorists who continue sporadic violence against U.S. troops.

But some officers said the hostile forces were making gains by acquiring more advanced weaponry, such as armor-piercing munitions, and improving their training and organization.

Asked whether conditions in southern Afghanistan are more dangerous than earlier in the conflict, Capt. Matthew Harmon, commander of headquarters company, 1st Battalion, 3rd Special Forces Group, said in an interview, “That’s a very fair assessment.” Harmon is serving his fourth tour in Afghanistan.

Capt. Chris Sample said the 1st Battalion had engaged in 88 firefights in the past six months. That is more than in its three previous Afghanistan deployments combined, he said. There also has been a recent increase in vehicle-borne suicide bombers, he said.