KANDAHAR, Afghanistan (Reuters) - U.S. warplanes unleashed three strikes on Friday in Afghanistan's province of Uruzgan, where Afghan security forces remained surrounded by Taliban fighters a day after having fought back a concerted push by the militants.

The Taliban attack, in one of the country's top opium-producing areas, has exposed how thinly stretched Afghan security forces have become as they try to contain Islamist insurgents in other areas of the country.

Taliban insurgents on Thursday battled their way to within a few hundred meters (yards) of key government buildings in Tarin Kot, a city of about 70,000 and capital of the south-central province, while many local leaders fled to a nearby airport.

In the capital, Kabul, the American military command confirmed that its warplanes had conducted at least three air strikes, with aircraft of the Afghan air force also providing support.

Bolstered by reinforcements and air support, Afghan troops pushed the Taliban out of the city by nightfall, but the situation remains serious, said Dost Mohammed Nayab, a spokesman for the Uruzgan governor.

"The Taliban are still in surrounding areas of the city," he said. "Our forces are exhausted and are running short of ammunition." 

Overnight clashes left at least seven dead on the government side and 30 among the Taliban, said Abdul Karim, head of the Uruzgan provincial council.

He accused the Taliban of using civilians as human shields, complicating efforts to drive out the insurgents. "It will take more attention and effort to clear all areas," he added.

The Taliban on Thursday rejected government officials' claims of high casualties among the attackers, saying in a statement they had overrun more than a dozen checkpoints and seized many weapons and other equipment from retreating troops.

Photos posted online by the Taliban purport to show fighters looting and burning what appears to be a government military base.

About 16,000 NATO and allied troops remain in Afghanistan, mostly in advisory and counter terrorism roles, but also regularly launching air strikes in support of Afghan operations.

At least 69 coalition troops died in Uruzgan during nearly a decade and a half of international military efforts to defeat the Taliban and other militant groups after 2001.

The province is in a part of Afghanistan long dominated by the Taliban and warlords who vie for access to its lucrative smuggling routes and illicit drug production.

(Reporting by Sayed Sarwar Amani; Writing by Josh Smith; Editing by Clarence Fernandez)