Mr Maduro said he had evidence that right-wing Venezuelan poluticians had been involved in the plot.
He has alleged conspiracies against him since taking over from the late President Hugo Chavez and winning disputed elections last month.
Mr Uribe – a fierce critic of President Chavez – dismissed Mr Maduro’s accusation as “immature”.
On Friday, Mr Maduro said: “Uribe is behind a plot to kill me. Uribe is a killer.
“I have enough evidence of who is conspiring, and there are sectors of the Venezuelan right involved,” Mr Maduro added.
Hours later, Mr Uribe responded by saying: “To the immature accusation by the dictatorship… just one response: repeat the elections.”
Mr Maduro won the 14 April poll by a narrow margin of 1.49%, according to the official results.
Venezuelan opposition leader Henrique Capriles is challenging the result, alleging irregularities.
During his term in office Alvaro Uribe clashed with Hugo Chavez on a number of issues.
Mr Uribe, a conservative, stepped down in 2010.
Ties between the two neighbouring countries have been steadily improving since then.