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In Islamabad, a Pakistani official said his government would like evidence against Mr. Saeed and Mr. Makki.

Pakistan would prefer to receive concrete evidence to proceed legally rather than to be engaging in a public discussion on this issue,” said Abdul Basit, a spokesman for Pakistan’s Foreign Office.

This evidence must withstand judicial scrutiny, he added.

The State Department’s action has incensed Pakistan, but India has welcomed the move. The nuclear-armed South Asian neighbors have fought three wars since 1947.

“The bounty marks a clear indication of the U.S. showing that if the Pakistanis continue in their incessant demands, Washington has an Indian card to play,” said Marvin Weinbaum, a former State Department analyst for Pakistan and Afghanistan who is currently at the Middle East Institute.

“It has laid down a marker that we’ve had about enough of simply being on the receiving end of demands and threats, where the government and public opinion are doing the military’s bidding in shaping the relationship with the U.S.”

The bounties on Mr. Saeed and Mr. Makki threaten to further strain tense U.S.-Pakistani ties. Pakistan’s parliament is debating a reset in the relationship, which has been hit by multiple crises since January 2011.

Mr. Saeed lives in Pakistan’s eastern city of Lahore. With his fiery anti-U.S. and anti-India speeches, he has emerged as a galvanizing force in the Defense of Pakistan Council, an alliance of religious and extremist groups. The group regularly organizes public rallies attended by gun-toting jihadists.

Mr. Saeed is opposed to U.S. drone strikes against terrorist suspects in Pakistan and has warned of a violent reaction around the country if the Pakistani government reopens supply routes to NATO troops in Afghanistan.

Pakistan shut these routes to protest an attack by NATO on two of its border posts that killed 24 Pakistani soldiers in November.

Meanwhile, U.S. Deputy Secretary of State Thomas R. Nides on a visit to Islamabad acknowledged the challenges bedeviling the U.S.-Pakistani relationship but said “too much is at stake for us to turn away from each other.”

He met with Foreign Minister Hina Rabbani Khar on Wednesday.