WASHINGTON - NATO defense ministers signaled broad support Friday for a robust counter-insurgency strategy in Afghanistan, adding to the momentum in favor of proposals for a substantial U.S. troop hike. Without discussing troop levels, NATO ministers meeting in Bratislava, Slovakia, endorsed the strategy put forward by Gen. Stanley A. McChrystal, the U.S. and allied commander. The alliance rejected competing proposals to narrow the military mission to simply fighting the remnants of Al Qaeda. "The only way to ensure that Afghanistan does not become once again a safe haven for terrorism is if it is made strong enough to resist the insurgency as well," said Anders Fogh Rasmussen, the NATO secretary general. "In Afghanistan, you cannot separate counter-terrorism from counter-insurgency." As the Obama administration reviews U.S. strategy, the NATO endorsement is likely to add impetus to McChrystal's request for 40,000 additional troops to protect the Afghan people, shore up the government and counter Taliban militants. It is unlikely the defense ministers would have issued such an unambiguous endorsement of McChrystal's plan without at least the tacit approval from U.S. officials, who maintain close contact with NATO member governments on the issue. Defense Secretary Robert M. Gates attended the meeting but made no attempt to counter the move by the ministers to throw their backing behind McChrystal. Gates is considered a supporter of McChrystal, but has avoided publicly discussing his views, including in Bratislava. "I was in a listening mode," Gates said at a news conference. "We are here to consult." The NATO ministers' support could prove crucial to the White House. Showing that the administration has the support of its allies would be critical to Obama's ability to make his case for a troop increase to the U.S. public. The endorsement came at a time of increasing confidence among military and other government officials in Washington that the administration will agree to much of McChrystal's troop request. It also came days after developments in Afghanistan's presidential election promised to clear another potential hurdle to a troop increase. President Hamid Karzai's acceptance of a runoff election could provide the Afghan government with the legitimacy experts say is essential to McChrystal's strategy. Together, the Afghan runoff and the NATO endorsement undercut proposals by U.S. Vice President Joe Biden and others to focus more on hunting terrorists than on defeating the Taliban-led insurgency in Afghanistan. "It does not solve the problems in Afghanistan just to hunt down and kill individual terrorists," Rasmussen said. "What we need is a much broader strategy." Obama administration officials have been reviewing their strategy for the last six weeks. Gates said the analytic phase of the internal deliberations were nearly finished, and said specific options would be discussed over the next "two to three weeks." The final decision by Obama could come right before or soon after the Nov. 7 run-off between Karzai and his challenger, Abdullah Abdullah, the former foreign minister. The runoff is important to U.S. plans because a legitimate government in Kabul is seen as critical to the success of a counter-insurgency plan. Controversy surrounding election fraud from the country's August ballot fueled White House interest in reopening the strategy debate. As part of the NATO meeting, Gen. Stanley A. McChrystal, the top allied commander in Afghanistan, offered a 15-minute report to the defense ministers on his assessment of the war. Actual troop commitments will not be discussed by NATO until November, but Gates said a number of allies indicated they were thinking about increasing their own military or civilian contributions. "I detected a commitment and an energy on the part of our allies, both in uniform and civilians, in terms of their determination to participate with us in Afghanistan and see this through to a successful conclusion," Gates said. The NATO meeting posed challenges both for the Obama administration and its NATO allies, said Rick Nelson, a senior fellow at the Center for Strategic and International Studies. It gave the administration a critical opportunity to keep allies on board during the White House strategy review. For the alliance, it showed Afghanistan remains a crucial test. "The success of Afghanistan is tied to the success of the post-Cold War NATO," Nelson said. "So they want to be successful. Cutting and running won't play into anyone's favor." But at news conferences following the NATO meeting, several officials expressed hesitancy about committing additional resources until a new government is in place. "We have to make sure the new government in Afghanistan are committed to their job before we send any more troops," said Soeren Gade, the Danish defense minister. Rasmussen said standards for the next round of voting in Afghanistan must be higher than those followed in the tainted August balloting. "Considering what we are investing in Afghanistan, we also have the right to insist on it," he said. NATO countries have about 38,000 troops in Afghanistan fighting alongside 68,000 Americans. U.S. and allied officials increasingly appear to agree on the need for additional troops for training Afghan forces. McChrystal favors a new target of 400,000 Afghan security forces, up from the current goal of 230,000. U.S. defense officials have said a sizable portion of McChrystal's troop request is for forces directly involved in speeding up the training. Rasmussen said the training mission requires additional teams and more money, but represents the alliance's long term exit plan. At the same time, he said the alliance must plan to give Afghans the lead on security matters. "We have not yet agreed to start handing over the lead. The conditions are not yet right," he said. "But transition will happen, district by district, when the conditions are right." Julian.Barnes@latimes.com