PESHAWAR, Pakistan (Reuters) - Taliban militants recovered 24 bodies and were searching for more on Friday, hours after suspected U.S. drones destroyed a camp in Pakistan's northwestern region, militants and officials said.

Four missiles believed to have been fired by at least two pilotless U.S. drone aircraft on Thursday evening hit a militant hideout and training camp in the Kurram tribal region on the Afghan border.

Soon after the attack a villager in the Barjo area said 14 people had been killed but an intelligence official and a Taliban official said on Friday the toll had gone up as militants sifted through the rubble of the seven-room training compound.

We've so far found 24 bodies in the debris and we're still looking, a Taliban official in the ethnic Pashtun region said by telephone. He declined to be identified.

Pakistani security agents and the militant official said there were no senior militants, or high value targets among the dead. The Taliban official said those killed were Pakistani and Afghan.

U.S. drones have carried out more than 30 drone strikes since early 2008 when the United States, frustrated by an intensifying insurgency in Afghanistan getting support from the Pakistani side of the border, began attacking with greater frequency.

Eliminating militant support from the lawless northwestern Pakistani enclaves is seen as essential for winning the war in Afghanistan.

There has been no let-up in the strikes since the administration led by President Barack Obama took over in January, with six strikes since then, despite complaints from the Pakistani government.

Pakistan's civilian government, elected a year ago, and the army have complained that the U.S. missile strikes are counterproductive and the civilian casualties they often inflict have fueled support for the militants.

The drones, which have mostly struck in the North and South Waziristan regions, to the south of Kurram, have killed several mid-level al Qaeda members.

Pakistani Foreign Minister Shah Mehmood Qureshi, unable to persuade the United States to stop the strikes, said last month he had asked the U.S. to transfer the unmanned aircraft to Pakistan.

Qureshi was in Washington to take part in the Obama administration's review of policy on Afghanistan and Pakistan.

The administration aims to have the main outlines of the strategy drawn up before a March 31 international conference on Afghanistan and a NATO summit in early April.

(Reporting by Alamgir Bitani; Writing by Augustine Anthony; Editing by Robert Birsel and Sanjeev Miglani)