A statement issued by the presidential palace said Obama agreed in a video call to start talking about a review, which Karzai also proposed in a letter.

"The two presidents agreed that discussions regarding a strategic review of the more effective ways of fighting terrorism should begin," the statement, written in Dari, said.

"The war on terrorism should not be won in the villages of Afghanistan, there should be a strategic review of the method of fighting terrorism," it said, adding they also discussed the parliamentary election on September 18 and efforts to combat corruption.

Civilian casualties caused by U.S. and other foreign forces have been a source of friction between the Afghan government and its Western backers and led to a serious dispute between the two sides last year.

With a parliamentary election looming after a flawed presidential poll a year ago, Karzai is under pressure to demonstrate independence from his Western backers.

He has pushed reconciliation efforts with insurgents through a peace plan which includes an offer of an amnesty, cash and job incentives to Taliban fighters.

Last month, online whistleblower Wikileaks published tens of thousands of classified documents about the war.

Wikileaks says it will publish about 15,000 more documents, ignoring demands by Washington to remove the material and return documents to the U.S. government.

CIVILIAN SUFFERING

The White House said on Friday the leaders discussed efforts to avoid civilian suffering as well as the campaign to defeat the Taliban. It said General David Petraeus, commander of U.S. and NATO forces in Afghanistan, and U.S. ambassador Karl Eikenberry also took part in the call.

"Both leaders agreed that the United States and Afghanistan should continue to work together to keep the pressure on the Taliban and to build Afghan capacity," the White House said in a statement.

Such deaths, often caused by air strikes, have angered ordinary Afghans who bear the brunt of the conflict.

General Stanley McChrystal, the former commander of U.S. and NATO forces in Afghanistan, issued a new tactical directive last year to limit the use of air strikes after a series of incidents involving civilians. That directive has been tightened even further since Petraeus replaced McChrystal in June.

A U.N. report issued this week said civilian casualties had risen 31 percent in the first six months of this year, with 1,271 killed. It said Taliban and other insurgents were responsible for 76 percent of casualties.

Deaths caused by "pro-government forces" fell to 12 percent of the total from 30 percent in the same period last year, mainly as a 64 percent fall in deaths caused by aerial attacks.

NATO forces have launched much fewer air strikes due to the tactical directives from issued by the U.S. commanders.

Fighting in Afghanistan has intensified despite the presence of almost 150,000 foreign troops. U.S. forces are preparing to start staged withdrawals from July 2011.

(Reporting by Andrew Hammond; Editing by Paul Tait)