Blair, who represents the quartet of intermediaries in the Middle East peace process - the United States, United Nations, European Union and Russia - was at the border Tuesday when he called off his visit to the Hamas-controlled Gaza Strip "due to a specific security threat."
Hamas spokesman Taher al-Nunu said: "Israel exerted great pressure to prevent Tony Blair from visiting the Gaza Strip because they did not want him to see the size of the disaster caused by the unjust blockade."
The envoy was due to tour a waste water treatment plant being built in northern Gaza with international funds and meet with humanitarian activists.
The Gaza office of the UN agency aiding Palestinian refugees said the cancellation of Blair's visit was a great disappointment.
Blair's agenda did not include meetings with officials from Hamas, which grabbed power in Gaza from President Mahmoud Abbas's Fatah party in street hostilities in June 2007. Hamas is considered a terrorist group by the U.S., the EU and Israel, but it said it had arranged security measures for Blair's time in Gaza.
Isolated by Israel and Egypt almost continuously since last summer over sporadic rocket attacks on Israel, Gaza has been suffering energy supply and humanitarian problems. Blair's visit would have been the first by a top Western official since the Hamas takeover that left Fatah in control of only the West Bank.