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The $10 million bounty puts Mr. Saeed in the same league as the one-eyed Mullah Omar. Only al Qaeda leader Ayman al-Zawahri commands a larger reward, with $25 million offered for information leading to his arrest.

The State Department also is offering up to $2 million for information leading to the location of Hafiz Abdul Rahman Makki, Mr. Saeed’s brother-in-law and Lashkar-e-Taiba’s second in command. Mr. Makki helped raise funds for Lashkar-e-Taiba and was already the subject of U.S. sanctions.

Lashkar-e-Taiba and Jamaat-ud-Dawa have powerful backers in Pakistan’s military, its Inter-Services Intelligence agency and among politicians.

“It’s no secret many in Pakistan consider [Lashkar-e-Taiba] an important tool in their country’s national security kit,” said the U.S. official. “The relationship is complicated by Pakistan’s attempts to constrain the group while preserving it as a reliable proxy.”

India has been Lashkar-e-Taiba’s traditional target, but the group has developed a more anti-Western agenda in recent years.

“The group has dipped its toe in the jihad against the U.S. and its allies outside South Asia, but it is far from fully committed to it,” Mr. Tankel said.