Mumtaz Qadri, a former police commando, killed Taseer with his official gun in Islamabad in 2011 for criticising the controversial blasphemy laws.
The blood money was offered after Islamabad High Court on Monday rejected his appeal against conviction by a lower court and upheld his death penalty.
Shaan Taseer, the son of slain governor, rejected the offer in a statement.
"On behalf of my family, I would like to state in no unclear terms that any such offer will be taken as an affront to the memory of my father, who laid his life down for a principle. There shall be no discussion on the topic of blood money with me or any member of my family," he said.
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"We are ready to pay much more Khoonbaha (blood money) to the family of Salman Taseer (for Qadri's release)," said JUP leader Shabbir Abu Talib said yesterday in Karachi.
He cited the case of CIA contractor Raymond Davis who was freed after paying blood money to families of two men he killed in Lahore in 2011.
According to Islamic law, a killer can be pardoned by the legal heirs of the victim with or without taking blood money.
Shaan said the religious parties are "strongly requested not to entertain the thought of making such an offer".
"Further, the parties have mentioned that they are 'ready for a healthy debate on the Mumtaz Qadri issue'. I welcome this offer wholeheartedly on the understanding that such a dialogue will include a debate on the Blasphemy Law, and not on blood money," he said in the statement.
"If the parties are serious about a 'healthy debate' they must first openly condemn the use or the threat of violence against any person or party that disagrees with their viewpoint.