The president said he believed that the people involved had fled to Florida, Peru and Colombia.
The Venezuelan leader regularly accuses the US of wanting to overthrow him.
The two countries have long had a tense relationship. When Mr Maduro was re-elected in May, the US increased its sanctions on Venezuela, saying the vote had not been free or fair.
However, in a televised address late on Saturday, President Maduro surprised many by saying he would accept US help to investigate the alleged plot.
“If the US government offered, or confirmed its offer, of FBI co-operation to investigate, I would accept it,” he said.
Mr Maduro said there were “terrorist” cells in Florida, which had masterminded the plan and needed to be dismantled.
He also called on the Peruvian government to extradite suspects living there.
What happened in the alleged attack?
The incident happened when Mr Maduro was speaking at military parade on 4 August.
Video footage showed the startled president looking…