The condemnation by a U.S. State Department official follows a statement by a spokesman for the Pakistani prime minister disassociating his government from Bilour's offer relating to the video that has triggered widespread protests in the Muslim world, including Pakistan where several people have died in various cities, the BBC reported.
"The president and secretary of state have both said the video at the core of this is offensive, disgusting, and reprehensible -- but that is no justification for violence, and it is important for responsible leaders to stand up and speak out against violence," a U.S. State Department official told the BBC.
"Therefore we find Mr. Bilour's announcement is inflammatory and inappropriate. We note that the prime minister's office has dissociated itself from his comments."
The BBC quoted Bilour as saying: "I will pay whoever kills the makers of this video $100,000. If someone else makes other similar blasphemous material in the future, I will also pay his killers $100,000.
"I call upon these countries and say: Yes, freedom of expression is there, but you should make laws regarding people insulting our prophet. And if you don't, then the future will be extremely dangerous."
The New York Times had reported a top aide to Bilour as saying subsequently that the minister was trying to diffuse frustration and anger in the streets in Pakistan.
"We completely dissociate ourselves from the statement of Mr. Bilour," Shafqat Jalil, press secretary to Prime Minister Raja Pervez Ashraf, had been quoted as saying.
The BBC said while the origins of the anti-Islam video called "Innocence of Muslims," remained unclear, its alleged producer of the video's trailer remained in hiding.
The U.S. government has advised its citizens not to travel to Pakistan. The U.S. Embassy in Islamabad had provided paid announcements on Pakistani television showing U.S. President Barack Obama and Secretary of State Hillary Clinton condemning the film.
Jalil was quoted by the BBC as saying Bilour was not a member of the ruling Pakistan People's Party, and that the prime minister would speak to Bilour's party, which is part of the ruling coalition.