The US military has been questioning about 20 people in Iraq suspected of having al-Qaeda links, the US says.
Lieutenant-General Sanchez said the insurgency had intensified
US troops have detained a number of foreign nationals in the country, Lieutenant General Ricardo Sanchez, the commander of US forces, said.
"We are seeing Yemenis, Sudanese, Syrians and Egyptians, to name a few," he said on Tuesday.
The disclosure came as the chief US administrator in Iraq, Paul Bremer, unexpectedly left for Washington.
He said earlier he was considering creating an Iraqi security force able to spot foreign fighters in Iraq.
Meanwhile, the interim foreign minister in Iraq, Hoshyar Zebari, has called for a new security force to be set up composed of groups that opposed Saddam Hussein and his regime.
In continuing violence, police said four Iraqi civilians were killed by a roadside bomb in the southern city of Basra.
And a series of eight explosions were heard in Baghdad with reports of smoke rising from close to the American headquarters compound beside the River Tigris.
Security force mooted
In an interview with Reuters news agency, Mr Zebari said the security force he was proposing would "hunt down Baathist loyalists, within the law, but with a tougher approach".
"Security responsibilities need to be handed over to
dedicated, politicised Iraqis who are committed to the new
"We need to show people
that there is a visible Iraqi authority in the street," he said.
On Monday, Mr Bremer said he was considering creating a force partly composed of Kurds and Shias, who would be able to spot foreign fighters in Iraq.
The BBC's Peter Biles in Baghdad says it has long been suspected that Islamic militants have been slipping into Iraq to join the opposition to the US-led occupation of the country.
Mr Bremer left Iraq for the United States at short notice on Tuesday, cancelling a meeting with visiting Polish Prime Minister Leszek Miller.
A spokesman for Mr Bremer said the governor would return in a few days, without giving any explanation for his trip, AFP news agency reported.
General Sanchez told reporters in Baghdad there was no doubt that the insurgency against US-led forces in Iraq had intensified.
Guerrilla fighters had "developed their capability" in recent attacks, using rockets and mortars.
The US commander said more than 5,000 people are now in detention and that the Americans have been interrogating as many as 20 people thought to be linked to al-Qaeda, although no proof had been found.
When asked how close US forces had come to capturing former Iraqi leader Saddam Hussein, General Sanchez replied: "Not close enough."
The explosion in Basra blew up a civilian car
Nearly 150 US soldiers have been killed in Iraq since President George W Bush declared an end to major combat operations in May.
General Sanchez was speaking a few hours after the four Iraqi civilians were killed by a bomb in the southern city of Basra.
The explosion, which took place on a road used frequently by British troops, blew up a civilian car and damaged other vehicles.
British forces quickly sealed off the area, but no British troops were reported to be in the area at the time of the explosion, which happened at about 0830 (0530 GMT).
British units in Basra have been periodically hit by violence but not on the scale of attacks suffered by US troops in the north and west of Iraq.
The BBC's Kim Ghattas says British troops on patrol in the mainly Shia Muslim area are still met with smiles and extended hands, a sight not common any more in Baghdad.