BAGHDAD, Iraq -- U.S. forces battled the tattered remnants of Iraq's army for control of downtown Baghdad Tuesday, crushing a counterattack and seizing a military airport.

Saddam Hussein's fate was unknown after an attempt to kill him, his two sons and other Iraqi leadership figures from the air. (Full Story.)

EYE ON IRAQ Full Coverage: Iraq War Interactive: How We Got Here Section: President Obama Survey: Support Obama's Iraq Strategy?

Inside the capital to stay, some Army units routed Iraqi fighters from a Republican Guard headquarters. Others discovered a 12-room complex inside a cave, complete with white marble floors, 10-foot ceilings and fluorescent lighting.

Marines battled snipers as they fought deeper into the capital from the east. They seized the Rasheed Airport and captured enough ammunition for an estimated 3,000 troops. Ominously, they also took a prison where they found U.S. Army uniforms and chemical weapons suits possibly belonging to U.S. prisoners of war.

Coalition strikes have knocked Iraqi TV off the air. It's been one of main ways the Iraqi regime has communicated with a population increasingly eager to help coalition troops.

Earlier, American forces crushed a counterattack by about 500 Iraqi fighters. At least 50 of them reportedly were killed.

During the Iraqi counterattack, apparently in response to the strike on the Iraqi leader, buses and trucks full of fighters crossed the Tigris River in an attempt to overrun U.S. forces holding a strategic intersection on the western side of Baghdad.

U.S. troops strafed the Iraqis from A-10 Warthog attack planes and opened up with artillery and mortar fire. Snipers reportedly wounded two American soldiers, one seriously.

Earlier, troops with the Army's 101st Airborne Division launched an attack on an eight-story former Republican Guard headquarters about half a mile from the airport. Two Iraqis were reported killed in the gun battle. There were no U.S. casualties.

Pentagon: Republican Guard Still Receiving Orders

Pentagon officials said Tuesday they can't say whether Saddam was killed in the bunker-buster bombing of buildings in Baghdad, but that command orders are still being issued to key elements of Iraq's military.

Maj. Gen. Stanley McChrystal told reporters at Tuesday's Pentagon briefing that the elite troops appear to be following orders from someone -- perhaps from Saddam himself.

But, he said, the Republican Guards are getting orders and not following them, and in many cases are unable to follow them.

"So they're not an effective fighting force," he said.

Still, McChrystal said, it appears as though Saddam may still be in control of elements of the guard -- as well as some death squads.

McChrystal added that elements of the Special Republican Guard, the division that ordinarily fights in Baghdad, still operates in the Iraqi capital "and is capable of sharp fights."

Northern Iraq Fighting Slows

Fighting on Iraq's northern front is cooling somewhat as battles in Baghdad heat up. An Associated Press reporter in northern Iraq said the fast-moving events in Baghdad have given some pause to the fighting up north.

The reporter said allied commanders in the north are hoping that if allied forces tighten their grip on the Iraqi capital, then the two key cities in northern Iraq, Mosul and Kirkuk, may fall without much of a fight.

But the northern fighting hasn't stopped completely. Allied airstrikes are still hitting some Iraqi targets, and U.S. special forces troops have fanned out along the front lines to monitor Iraqi movements. But the reporter said neither side has made significant advances.

Latest Developments Thousands Of Iraq Museum Items Found 250 Iraqi Prisoners Released By U.S. In Iraq Report: Saddam Sent Son To Raid Iraq's Central Bank Iran Rips U.S. Truce With Mujahedeen Leading Iraqi Bioweapons Scientist In U.S. Custody