The Fanatics boasted on the internet that "brothers were preparing through the night to destroy his convoy" in Gaza.
They branded Blair, who is now Middle East envoy, as a "criminal" and "the enemy of God".
"Oh God, the idea occurred to me of kidnapping him and slaughtering him," The news paper quoted one fanatic, Hamza al-Ghamdi as saying on an Arabic website.
A spokesperson of Blair said on Tuesday that the visit was cancelled because of a "specific security threat". She did not give details.
He would have been the most highly ranked international diplomat to visit the strip since the militant movement Hamas took control there in 2007.
Blair was expected to meet with traders and inspect a northern Gaza waste water project being built with international funds.
Blair was due to meet UN officials to discuss humanitarian work in the strip and visit a water treatment plant.
He had not been expected to meet any representatives from Hamas.
The international community does not recognise the Hamas government in Gaza.
The European Union, the United States and Israel consider Hamas to be a terrorist organisation.
The movement seized control of Gaza in June 2007 from Fatah forces loyal to the Palestinian Authority President Mahmoud Abbas.
The former British Prime Minister was appointed as Middle East envoy in the same month by the Quartet the US, the EU, the UN and Russia.
Source: by DDNEWS
