The United States has offered a $10 million US bounty for the founder of the Pakistani militant group blamed for the 2008 attacks in the Indian city of Mumbai that killed 166 people, a move that could complicate U.S.-Pakistan relations at a tense time.

Hafiz Saeed founded Lashkar-e-Taiba in the 1980s, allegedly with Pakistani support to pressure arch-enemy India over the disputed territory of Kashmir. Pakistan banned the group in 2002 under pressure from the U.S. but has done little to crack down on its activities.

Saeed operates openly in the country, giving public speeches and appearing on TV talk shows. The U.S. also offered up to $2 million for Lashkar-e-Taiba's deputy leader, Hafiz Abdul Rahman Makki.

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Hafiz Saeed, shown in 2011, operates openly in Pakistan, giving public speeches and appearing on TV talk shows. (K.M. Chaudary/AP)

The bounties were posted on the U.S. State Department Rewards for Justice website late Monday, the U.S. Embassy in Islamabad said Tuesday.

The reward for Saeed is one of the highest offered by the program and is equal to the amount for Taliban chief Mullah Omar. Only Ayman al-Zawahri, who succeeded Osama bin Laden as al-Qaeda chief, fetches a higher, $25 million bounty.

U.S. Undersecretary of State Wendy Sherman announced the bounty for Lashkar-e-Taiba's leader and deputy on Monday during a visit to India, according to The Times of India newspaper.

The move comes at a particularly tense time in the troubled relationship with the U.S. and Pakistan. Pakistan's parliament is currently debating a revised framework for relations with the U.S. in the wake of American airstrikes that killed 24 Pakistani soldiers in November at two posts along the Afghan border.

Pakistan retaliated by kicking the U.S. out of a base used by American drones and closing its border crossings to supplies meant for NATO troops in Afghanistan.

The U.S. hopes the parliamentary debate will result in Pakistan reopening the supply lines. The closure has been a headache for the U.S. because it has had to spend more money sending supplies through an alternate route that runs through Central Asia. It also needs the route to withdraw equipment as it seeks to pull most of its combat forces out of Afghanistan by the end of 2014.

But it's unclear whether the U.S. will be willing to meet Pakistan's demands, which include higher transit fees for the supplies and an unconditional apology for the airstrikes, which the U.S. has said were an accident. Pakistan has also demanded an end to American drone strikes in Pakistan, but it's unclear if that will be tied to the reopening of the supply line.