Less than a mile from the scene of Monday's suicide bombing, Coe was among hundreds of people who lined a specially constructed street track to see stars competing, including Australian former Olympic champion hurdler Sally Pearson and British long jumper Greg Rutherford.
The City Games went ahead amid tight security, with Britain's terror threat level raised to critical after the blast that killed 22 people at the Manchester Arena. Thousands of runners will also take to the Manchester streets on Sunday for a half marathon and 10-kilometer race.
"It's not the only solution, but at this very moment there are coaches working the length and breadth of the country in some really challenged communities and that's what sport does all the time. Maybe this is a really important time for sport to be involved in that process."
The head of track and field's governing body recalled watching "with mounting horror" from IAAF headquarters in Monaco as news of the atrocity unfolded at the Ariana Grande concert.
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"Like many people, we felt we just needed to be here," said Coe, the double middle-distance Olympic champion.
Security in Britain is high on the IAAF agenda, with London hosting the world championships in August at the Olympic Stadium.
"I know the diligence and forensic work (by the security services), our police services are outstanding," said Coe, who headed the 2012 London Olympics organizing committee.
"They're the best in the world. You've only got to see the way they responded here (on Monday) and the work that we did in London with those teams.