WASHINGTON (Reuters) –
NATO chief Anders Fogh Rasmussen assured U.S. President Barack Obama on Tuesday the alliance would remain in Afghanistan as long as it took to finish its mission.

"Our operation in Afghanistan is not America's responsibility or burden alone: it is and it will remain a team effort," the former Danish prime minister told reporters during a visit with Obama at the White House.

Rasmussen said he agreed with Obama's approach of "strategy first, then resources."

"This alliance will stand united and we will stay in Afghanistan as long as it takes to finish our job," he added.

Obama, who is meeting top advisers about Afghanistan on Tuesday and Wednesday, has said he will not decide on sending further U.S. troops for Afghanistan until after a broad review of strategy. He did not discuss that process during their brief appearance before reporters.

The top U.S. and NATO commander in Afghanistan, Gen. Stanley McChrystal, has warned the Afghan effort would likely result in failure without a "significant change in strategy", which would also involve bringing in more troops.

He is expected to seek 30,000 to 40,000 combat troops and trainers, according to defense and congressional officials.

(Reporting by Jeff Mason; Editing by Simon Denyer)