The threat was delivered by Mario Vazquez Rana, the President of the Pan Am Sports Organization (PASO), who said that the Games, which are attended by 7,000 competitors and officials, were at level "red".

He said: "A lack of confidence is increasing.

"We have to continue knowing we are on red - every day, every hour.

"We have to watch hour by hour, day by day and week by week."

The PASO, the body which oversees the Games, asked local organisers for the $50 million (£30 million) guarantee several weeks ago when it became clear they were behind schedule building a stadium for athletics, an aquatic centre and an athletes' village.

Ten new venues are being planned, also including a volleyball arena, covered velodrome, shooting range, and a basketball arena.

Rana said: "The guarantee we asked for, to cover problems that might come up, was to be handed over today.

"It has not happened because of paperwork that is taking longer than expected.

"We are giving them 10 working days to come up with the guarantee."

Rana said today at the PASO Assembly that local organisers, who were chosen to host the Games in May 2006 when they were the only candidate, needed to hand over the guarantee by November 20.

He said: "Once we have the guarantee we'll let you know, and if not we'll have to figure out what to do.

"If they [organisers] fail, we'll cash the $50 million.

"The money is not important.

"What is important is the Games.

"We're doing this to put a little pressure on them."

The row has overshadowed the campaign to choose a host city for the 2015 Games, for which Bogota, Lima and Toronto are bidding.

The Games were last held in 2007 when Rio de Janeiro used them as a springboard for its successful bid to host the 2016 Olympics.