One of the strikes destroyed the home of Taleban leader Mullah Omar in Kabul, reportedly only 15 minutes after he had left.
General Myers said they would return to the few targets air surveillance showed they had missed.
Part of the next phase of military operations is an intensification of surveillance flights over the area by high-tech American and British planes seeking sightings of bin Laden or his men.
With the sky cleared, President George W. Bush formally notified the US Congress he would send further ground-based troops into the region.
His letter said it was not possible to predict the scope or duration of the military operation.
The bulk of the new force is expected to come from the 5300 US troops still in Kosovo and 3600 in Bosnia, partly because overseas troop deployments require training, certification such as wills and inoculations, and official clearances.
The Balkans-based units can be moved at any time and replaced by Nato troops.
The 101st Airborne Division and the 160th Special Operations Aviation Regiment will reportedly be sent from their Fort Campbell base in Kentucky on October 16.
The 101st was to be sent on peacekeeping duties in the Sinai Desert, but this has been cancelled.
The US is also doubling the 1000 troops of the Army's 10th Mountain Division already stationed in neighbouring Uzbekistan.
Subject to agreement by the Uzbek Government, this unit will be boosted by British troops from the 24,000-strong force taking part in Operation Saif Sareeya in Oman.
Uzbekistan is worried any long-term US military presence will anger its neighbours and drag it into the conflict.
The Taleban recently said it had moved troops to the Uzbek border and would attack if the country became a base for US strikes.
But the Government is receiving a diplomatic barrage from the US and Britain to encourage it to co-operate because the political situation in Pakistan may rule out further troops being based there.
Special forces units already in Pakistan will stay there, but all Army helicopters are likely to be transferred to USS Kitty Hawk which has arrived in the region without its usual 70 strike aircraft.
A further possibility is to station troops within Afghanistan.
The Russians built 220 airstrips in the country during their ill-fated war and have given details of their facilities to the US.
The most desirable is the all-weather air base at Bagram, a 3.2km runway 30km north of Kabul.
The Washington Post says commanders of units being sent into the region are being told their mission could last up to a year, although their role is being left vague.
Possibilities being suggested by US defence officials include large-scale short-term offensives inside Afghanistan or "force protection" where troops would be used to protect the bases of air units.
US Secretary of Defence Donald Rumsfeld left no doubt that troops would play a hostile role because the Taleban and al-Qaeda would not be beaten by air strikes alone.
"I think it's just terribly important to underline that and emphasise it so people don't go away with the mistaken understanding that some sort of a cruise missile is going to solve that problem, because it isn't."
But the problem beginning to face US planners is what to do if the Taleban does fall quickly.
Northern Alliance "foreign minister" Abdullah Abdullah yesterday predicted the radical regime would fall "in a matter of weeks, perhaps, if not days".
He claimed 1200 soldiers and commanders had defected and closed the only road linking north and south Afghanistan.
This left the Taleban with only one supply route, the road from the north-west city of Herat to Kabul.
Dr Steve Hoadley, a political lecturer at Auckland University, said British Prime Minister Tony Blair had already made it clear that Afghanistan would have to form its own government.
The likely make-up of any new government is difficult to predict and could have serious consequences for the region.
Dr Hoadley said Pakistan would keep a close eye on developments and would oppose any government formed around the rebel Northern Alliance, because they were mainly from areas hostile to Pakistan's Pashtun tribe and had sympathies towards India and Russia.
"That is why they are being so helpful," he said.
"Being a good ally will mean they are not left behind by India - their western border is very important."
