"The events that led to the Egyptian army's removal of President Mohamed Morsi confronted the military with a simple choice: intervention or chaos," wrote Blair, who led Britain for a decade from 1997.
The army toppled Morsi from power last Wednesday following huge protests against his rule, but dozens of people have been killed in clashes in the wake of his departure.
Blair said the West had strong incentives to support Egypt's democratic transition.
"At its crudest, we can't afford for Egypt to collapse. So we should engage with the new de facto power," he wrote.
"In that way, we can also help shape a path back to the ballot box that is designed by and for Egyptians."
Likewise, Blair argued that Western nations have a responsibility to work towards peace in the wider Middle East.
"We feel it should be someone else's job to help sort it out. But it is our job," he wrote.