Lord Ahmed, 53, who in 1998 became the first Muslim life peer, was reported to have made the comments at a conference in Haripur in Pakistan.
A Labour Party spokesman said: “We have suspended Lord Ahmed pending investigation. If these comments are accurate we utterly condemn these remarks which are totally unacceptable.”
According to Pakistan’s Express Tribune newspaper Lord Ahmed offered the bounty in response to a US action a week ago.
The US issued a $10 million reward for the capture of Pakistani militant leader Hafiz Mohammad Saeed, founder of the Lashkar-e-Taiba group, who it suspects of orchestrating the 2008 Mumbai attacks in which 166 people died as terrorists stormed hotels and a train station.
The British peer reportedly said: “‘If the US can announce a reward of $10 million for the (capture) of Hafiz Saeed, I can announce a bounty of £10 million (for the capture of) President Obama and his predecessor, George Bush.”