Burkina Faso has denied any responsibility.
Mauritania said ringleaders of a failed putsch in June 2003, who are suspected of plotting another coup earlier this month, are being sheltered and trained by Burkina Faso under the protection of an adviser close to President Blaise Compaore.
"Burkina Faso has only two choices - either hand over those involved in the putsch or pursue its aggression against our country," Mauritania's Defence Minister Baba Walad Sidi said on Friday.
Mauritania said it had foiled an attempted coup two weeks ago and arrested about 30 soldiers for planning to topple President Muaauya Walad Sid Ahmad Taya while he was on a foreign trip.
Responding to the charges, Burkina Faso's Security Minister Djibril Bassole said, "We formally deny any involvement on the part of Burkina Faso in the series of plots which has shaken Mauritania."
A former French colony, Mauritania has been ruled by Taya since he seized power in a coup in 1984.
Mauritanian officials say two renegade commando units had planned to launch the latest attack, one based in Burkina Faso, the other in Libya.
Officials, however, have stopped short of accusing Libya of direct involvement in the failed coup.