"In his bag we discovered a homemade explosive device. He admitted he planned to plant it on the route of the parade today," Micky Rosenfeld said.
March organisers said they cancelled a gathering in a park at the end of the route because they were unable to get a permit from the fire department.
The city's fire department was on strike and therefore could not deploy a fire truck to the park, as required by law.
Several hundred ultra-Orthodox protesters held a counter-demonstration in a separate part of Jerusalem on Thursday.
Ultra-Orthodox Jews protested against the gay
rally after a supreme court appeal failed [AFP]
The protest came after opponents to the Gay Pride march failed in their appeal to Israel's supreme court that the event be cancelled.
At least 27 people were arrested in the ultra-Orthodox Jewish neighbourhood of Mea Shearim for throwing stones at police, Rosenfeld said.
Ultra-Orthodox Jews have rioted over the past week, burning tyres, assaulting policemen and damaging police cars.
Rosenfeld said 22 policemen were injured and 130 people arrested in the days before the parade.
The Jerusalem Gay Pride march is traditionally more muted than similar events in other global cities or the Israeli city of Tel Aviv.
At the 2005 Jerusalem march, an ultra-Orthodox man stabbed three marchers and last year’s parade was cancelled due to safety concerns.
Religious leaders in Jerusalem have routinely condemned the annual Gay Pride march, in contrast to sharp disagreements on most other political issues.