KABUL, Afghanistan – Afghan and Western troops have launched a new push into Taliban strongholds on the outskirts of Kandahar, Western military officials said Sunday, intensifying a months-long effort to dislodge insurgents from the southern city they regard as their spiritual home.

The offensive’s latest phase, dubbed Operation Dragon Strike, is centered on districts to the west and south of the city where Taliban fighters are deeply entrenched, military officials said.

“We expect hard fighting,” Brig. Gen. Josef Blotz, a spokesman for the North Atlantic Treaty Organization force, said in Kabul. Coalition troops, he said, were “destroying Taliban fighting positions so they will not have anywhere left to hide.”

For much of the spring and summer, Kandahar has been the focal point of NATO’s efforts to stabilize Afghanistan’s volatile south. Most of the soldiers and Marines sent in as part of the surge ordered by President Obama late last year have now been deployed in Kandahar and Helmand provinces, bringing American troop strength in Afghanistan to nearly 100,000.

But after months of trumpeting the planned Kandahar offensive, commanders retooled the strategy to place the emphasis on winning over the populace with better governance. The military component consists not of a drive into the city itself, but rather on choking off insurgents’ freedom of movement in and out of the metropolis of more than 1 million people.

The latest offensive — in which Afghan troops outnumber Western ones — is mainly taking place in the districts of Zhari and Panjwayi, Blotz said. He said it was preceded by weeks of so-called shaping operations “to soften insurgent defenses in preparation for the harder fighting,” which began early Saturday.

“Insurgents will be forced to leave the area, or fight and be killed,” Blotz said. “Either way, they will be separated from the Afghans they’ve intimidated for so long.”

Military officials said two Western troops were killed Sunday in a roadside bombing in the south, but did not specify whether they were taking part in the Kandahar campaign. With three months remaining, 2010 has already been the deadliest of the nine-year war for both U.S. troops and the NATO force as a whole.

Despite the Western aim of safeguarding civilian lives, the heightened tempo of fighting inevitably imperils villagers and townspeople in the south. The NATO force Sunday reported the fatal shootings of two Afghan civilians a day earlier in Helmand province, which borders Kandahar and has also been the scene of major clashes this year.

NATO’s International Security Assistance Force said in a statement that troops opened fire after the driver of a motorcycle and his passenger ignored warnings to stop, instead accelerating while approaching a “security perimeter.”