President Hamid Karzai (search) on Tuesday challenged the need for major foreign military operations in Afghanistan (search), saying airstrikes are no longer effective and that U.S.-led coalition forces should focus on rooting out terror bases and support networks.

His call for a new approach to tackling militants came despite the fiercest fighting in Afghanistan since U.S.-led forces invaded in late 2001, with more than 1,200 people killed in the six months leading up to Sunday's historic legislative elections.

Karzai demanded an immediate end to foreign troops searching people's homes without his government's authorization. He also said foreign governments should "concentrate on where terrorists are trained, on their bases, on the supply to them, on the money coming to them" — a veiled reference to support that militants allegedly get from neighboring Pakistan (search).

Afghan officials have repeatedly accused Pakistan of aiding Taliban rebels and other militants, a charge Islamabad vehemently denies.

"I don't think there is a big need for military activity in Afghanistan anymore," Karzai told reporters. "The nature of the war on terrorism in Afghanistan has changed now.

"No coalition forces should go to Afghan homes without the authorization of the Afghan government. ... The use of air power is something that may not be very effective now. ... That's what I mean by a change in strategy."

It was the second time Karzai has publicly challenged the U.S.-led coalition. In May, before a trip to Washington, he demanded more authority over the 20,000-member U.S.-led coalition here, but President Bush said they would remain under American control. In addition to the coalition troops, there are 11,000 NATO (search) peacekeepers in Afghanistan.

Karzai's comments coincided with the start of the count from the Sunday's parliamentary elections — the first here in more than 30 years. Trucks, helicopters and even donkeys were ferrying an estimated 6 million ballots to 34 counting centers around the country.

The polls are seen as a final step toward democracy on a path laid out in 2001, after U.S.-led forces ousted the Taliban for refusing to hand over Al Qaeda (search) leader Usama bin Laden (search) after the Sept. 11 attacks.

At a news conference in Washington, U.S. Defense Secretary Donald H. Rumsfeld (search) appeared to agree that airstrikes in Afghanistan might not be as useful as they once were.

"When you don't have a massed army on the ground or large puddles of enemies, then airstrikes are less effective than when you do have that type of a situation," he said.

Overall, however, Rumsfeld emphasized the country's ability to hold parliamentary elections without major violence, saying it marked a significant step toward stability.

"The country that hosted Usama bin Laden, that supported training camps for Al Qaeda, endured decades of civil war, Soviet occupation, drought, Taliban brutality, is now a democracy that fights terrorists instead of harboring them," Rumsfeld said.

White House press secretary Scott McClellan said the U.S. government works closely with the Afghan government and will continue to do so after Karzai's remarks on foreign military operations.

"These are all issues that we stay in close contact with them on and we'll continue to do so," McClellan said in New Orleans where President Bush was getting updates in Hurricane Katrina (search).

Karzai said he was "very, very satisfied" with the election.

But in a tape aired on Arabic television, Al Qaeda's No. 2 leader dismissed the vote as "nothing but a farce" held "under the terror of warlords" — an apparent reference to faction leaders in Afghanistan's destructive civil conflict of the 1990s, some of whom were candidates.

"Thieves and warlords are controlling affairs in the country, where international monitors can't observe more than 10 constituencies even if they wanted to," bin Laden's Egyptian deputy, Ayman al-Zawahri, said in a five-minute videotape aired late Monday on Al-Jazeera television.

Both Al Qaeda leaders are believed to be hiding along the rugged Pakistan-Afghan border.

Celebrations over the vote have been tempered by projections that turnout was just over 50 percent — down from 70 percent in presidential elections last October. The lack of any major Taliban assault to disrupt the vote Sunday was seen as a major boost to efforts to marginalize the rebels, though the insurgency shows no signs of waning.

In the latest fighting, guerrillas ambushed police patrols in southern Uruzgan and Zabul provinces Tuesday, sparking fire fights that left three officers and four militants dead and four officers wounded, officials said.

Hours before Karzai spoke, coalition commander Lt. Gen. Karl Eikenberry warned that he expected "more fighting in the weeks ahead."

"We are staying on the offensive against the enemies of Afghanistan, and we will continue that process throughout the fall and throughout the winter," Eikenberry said.

He said the United States is committed to helping Afghanistan with security and reconstruction so that terrorists cannot use it as a base.

But Karzai played down the militant threat, saying, "We do not think a serious terrorist challenge is emanating from Afghanistan." He did not specify whether he was referring to a threat from Al Qaeda terrorists, Taliban rebels — or both.