WASHINGTON – President Obama’s promised trip to Pakistan this year, once seen as a reward for a key ally in the fight against terrorism, is now a looming headache for the White House as it tries to determine whether the government in Islamabad was complicit in allowing Osama bin Laden to live for years in the country.

Obama told Pakistani officials in the fall that he planned to travel there in 2011, in part to soothe concerns that the president was favoring Pakistan’s neighbor and archrival, India, by visiting there first. White House spokesmen questioned last week refused to say whether Obama still planned to go.

In the hours after bin Laden’s killing by a U.S. special forces team in Pakistan, John Brennan, Obama’s top counterterrorism adviser, left the topic open: “I’m not going to address the president’s schedule.”

The decision is of enormous strategic and symbolic importance to both countries. A presidential trip would signal a continued U.S. commitment to its complicated, yet necessary, relationship with Pakistan, a country that is not only integral in dealing with terrorism, but will also play a key role in the U.S. troop drawdown in neighboring Afghanistan.

Canceling the visit could be seen as a sign of U.S. mistrust of Pakistan’s handling of extremists within its borders — bin Laden lived in what Brennan himself called within “plain sight” in a neighborhood home to many in the Pakistani military.