The offensive came up against heavy resistance
US defence sources said two 2,000-pound (907-kg) "thermobaric" bombs, which send suffocating blasts through cave complexes, were aimed at mountain caves where enemy fighters were hiding.
Afghan troops and US special forces fighting in the area had to pull back on Saturday after encountering heavy resistance. One US soldier and two Afghan allies were killed.
The fighting took place about 30 kilometres (20 miles) east of Gardez, the capital of Paktia province, and is said to be the biggest US-led ground operation of the whole Afghan campaign.
Thermobaric bombs were tested by the US in December and officials said in January that they would be rushed to Afghanistan for the campaign to root out supporters of Saudi-born dissident Osama Bin Laden.
Laser-guided, it is filled with a special explosive mixture that creates a high-pressure blast, driving all of the air out of a cave and potentially choking those inside.
Russia has used similar fuel-air bombs in Chechnya, causing international protests.
US intelligence had estimated that more than 500 al-Qaeda fighters were hiding in Paktia along with their families, but reports from the front suggest the total was much higher.
Reports said some troops had been cut off and surrounded as the al-Qaeda and Taleban fighters defended their high ground with mortars and heavy machine-guns.
The unnamed American killed is the third US combat casualty reported since the start of the Afghan campaign:
The assault came after the US announced it had intelligence that pockets of al-Qaeda and Taleban fighters were regrouping in the area.
Pakistan has sealed off a 100km (60 mile) stretch of its nearby border to stop militants escaping.
Fighters regrouping
A US military spokesman said American and Afghan forces were "moving methodically" to identify and eliminate al-Qaeda and Taleban fighters in eastern Afghanistan.
"Our goal since the beginning ... has been to eliminate al-Qaeda and Taleban elements in the country," said the 101st Airborne Division's Major A C Roper.
There are believed to be up to 5,000 foreigners who fought for the Taleban and al-Qaeda still inside Afghanistan.
The Pentagon said on Friday that hundreds of hostile fighters had gathered near Gardez after the collapse of the former Taleban regime at the end of last year.
"We don't know the make-up, but they're certainly not friendly," said Brigadier General John Rosa, deputy director of current operations of the Joint Staff.
The mountains around Gardez have been a hiding place for Afghan warriors since anti-Soviet guerrillas used them as a base for their fight against Soviet troops in the 1980s.
They have recently been identified as a possible refuge for fugitive Taleban leader Mullah Omar and Osama Bin Laden, widely blamed for the 11 September attacks on the United States.