Pakistan could wrap up the main phase of its anti-Taliban offensive in the Swat Valley within 10 days, a senior commander said Saturday, as the military confirmed the first kills in a new operation in the nearby tribal zone.

Pakistan is shifting the focus in its fight against militancy from the northwestern Swat Valley where troops have been pushing Taliban fighters back for almost two months to a new and much tougher battleground in the Afghan border region.

Washington supports both operations, and sees them as a measure of nuclear-armed Pakistan's resolve to take on a growing insurgency after years of failed military campaigns and faltering peace deals. The battle in the tribal region could also help the war in Afghanistan because the area has been used by militants to launch cross-border attacks on U.S. and other troops.

Maj. Gen. Sajjad Ghani, the commander of some 20,000 troops in the northern part of Swat where the area's top Taliban leader was based, told The Associated Press that some of the final strongholds were being cleared and that "high intensity" operations would end in a week to 10 days.

But stragglers could be expected to keep launching attacks on troops "for some time," he said.

"This area is the center of gravity for the terrorists," Ghani said, standing on a ridge overlooking the Piochar Valley where the Taliban leader in Swat, Maulana Fazlullah, once made his base.

"As of now, there are only pockets of resistance left. The terrorists are on the run. Command and control is in disarray. They are unable to organize an integrated response" to the army, he said.

The battle zone is strictly controlled, making it almost impossible to verify the military's description of events. Ghani spoke during a trip by a small group of journalists who were flown into the remote area by the army.

The military says it has made steady progress against the militants in Swat and surrounding districts since launching the operation in late April. Roads and some towns in the southern parts of the valley have been secured and some of more than 2 million residents displaced by the fighting will be allowed to return starting late this month, officials said.

In nearby South Waziristan, shelling and bombing of suspected militant targets has been stepped up and ground troops have been moving into position in the past week since the government announced the military would go after Pakistan's Taliban commander, Baitullah Mehsud.

South Waziristan is Mehsud's tribal stronghold, a chunk of the remote and rugged mountainous region along Pakistan's northwestern border with Afghanistan where heavily-armed tribesmen hold sway and Al Qaeda and Taliban leaders are believed to be hiding.

Although the army has not announced a formal start of full-scale operations in South Waziristan, officials said troops are already occupying strategic positions. Jet fighters flattened two abandoned militant-linked seminaries and a training facility Friday -- a further sign the operation was ramping up.

Two intelligence and army officials, speaking on condition of anonymity because they were not authorized to talk to the media, said there was heavy fighting Saturday in the villages of Barwand and Madijan and about 50 militants were killed -- the first confirmed militant casualties of the offensive in South Waziristan.

A military statement said 37 extremists died when troops retaliated after they tried to block the main South Waziristan road near the town of Sarwaki. There was no way to reconcile the differing death tolls due to restrictions on media access to the region.

Refugees would go first to Mingora, Swat's main city, where natural gas supplies and more than 500 phone lines have been hooked up, the military said. Residents would be allowed to go home in "phases," as power and civic facilities are restored, said Fazal Karim Khattak, a senior local government official.

Refugees staying in camps south of Swat worried about what they will find when they get home.

"Of course I am happy, but I don't know whether our home is safe or it has been destroyed," said Khadija Bibi, 45, a mother of four who left her home in Kanjua near Mingora in May.

Ghani said 95 percent of the 3,860-square mile (10,000-square kilometer) area under his control has been cleared of militants and most resistance now is coming in Biha, a short valley that backs into snow-covered mountains that are limiting the Taliban's efforts to flee.

He said about 400 militants have been killed in the area during the six weeks of fighting, but that many top commanders have managed to escape, including Fazlullah, and some were possibly headed toward havens in Afghanistan or South Waziristan.

Overall, the army says it has killed nearly 1,500 militants since April in Swat.

In Bajur, another trouble spot on the border with Afghanistan, the army shelled militant hide-outs and killed seven insurgents including a local commander, Gul Zarein, government official Jamil Khan said. The military declared victory over extremists there in February, but violence has flared again.