The tabloid, Britain's biggest selling daily, called for a referendum to be held as soon as possible.
The paper's political editor, Trevor Kavanagh, said Blair had "enraged allies in France and Germany by putting the whole EU edifice at risk by putting the constitution to a vote he cannot win."
The constitution must be ratified by all EU states to come into effect.
Reports have suggested that media baron Rupert Murdoch -- who owns the Sun and the Times -- has made it clear he could not support the re-election of a Labour government unless it offered a referendum.
The backing of the Sun was seen by many as crucial in helping Blair come to power in 1997.
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