A man who doused himself in an accelerant and set himself on fire outside the courthouse where former US president Donald Trump is on trial has died, police said.

The New York City Police Department said the man was declared dead by staff at an area hospital.

The man was in Collect Pond Park at around 1.30pm local time on Friday when he took out pamphlets espousing conspiracy theories, threw them around, then doused himself in an accelerant and set himself on fire, officials and witnesses said.

A large number of police officers were nearby when it happened. Some officers and bystanders rushed to the aid of the man, who was admitted to hospital in a critical condition.

The man, who police said had travelled from Florida to New York in the last few days, had not breached any security checkpoints to get into the park.

The park outside the courthouse has been a gathering spot for protesters, journalists and onlookers throughout Trump’s trial, which began with jury selection on Monday.

Throughout Friday, the streets in the area around the courthouse were generally wide open and crowds have been small and largely orderly.

Authorities said they were also reviewing the security protocols, including whether to restrict access to the park. The side street where Trump enters and leaves the building is off limits.

“We may have to shut this area down,” New York City Police Department Deputy Commissioner Kaz Daughtry said at a news conference outside the courthouse, adding that officials would discuss the security plan soon.