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A study published last spring by the Afghan Analyst Network, an independent policy research organization, said that expanding into the north and west strengthens the Taliban claim to be a legitimate national government fighting on behalf of the Afghan people and not simply the Pashtun community.

It also enables the Taliban to threaten NATO supply lines coming south from Central Asia. Those routes were established to reduce reliance on supply lines from Pakistan, which come under attack from fighters on both sides of the Afghan-Pakistan border.

“Furthermore, there is no doubt that the psychological impact of the north’s destabilization upon Western Europe and the U.S. would be considerable, overstretching resources as well as reducing the recruitment pool of Afghan army and police by enabling the Taliban to intimidate the families of volunteers,” the study said.

The psychological impact was evident in the reaction in Spain to the killing of the two trainers and the interpreter, a Spanish citizen of Iranian origin.

The leader of the small but important Catalan party Convergence and Union complained that Prime Minister Jose Luis Rodriguez Zapatero has avoided appearing in parliament as promised to hold a full-blown debate on the Spanish mission and must do so now.

The smaller United Left party called on Mr. Zapatero to bring Spain’s troops home, saying the NATO effort to defeat the Taliban and stabilize the country had achieved nothing.

The Spanish newspaper El Mundo published a cartoon Thursday showing President Obama and Mr. Zapatero standing chest-deep in a pool of quicksand labeled Afghanistan. Mr. Obama tells Mr. Zapatero: “It’s best to sit still, because if you move you sink even more.”

Also Thursday, NATO reported that three Afghan civilians were killed the day before by a homemade bomb in Kandahar’s Arghandab district, a Taliban stronghold near Kandahar city.

Two Taliban commanders were among a dozen militants killed Wednesday in fighting with a joint Afghan-coalition force in Uruzgan province, the Afghan National Police reported. Four insurgents were captured in the operation, the police said.

Associated Press writers Daniel Woolls in Madrid, Mirwais Khan in Kandahar, and Amir Shah and Christopher Bodeen in Kabul contributed to this report.