Theophile Mbemba, the interior Mmnister, said on Wednesday that the suspects, who were arrested on Tuesday, were former soldiers who worked for a Congolese security agency.
Mbemba said the men were arrested with military gear but did not provide details about the number or type of weapons.
They "were working in Kinshasa as security guards, but it is clear that they were military personnel with political plans," Mbemba said.
"They were part of a coup attempt, and they will face justice in Congo."
A UN official cast doubt on the accusation and said it was confident security would be maintained for the country's long-delayed polls, now set for July 30.
"We are not concerned about this, it appears to be a case of political manipulation by Congo's government," said Jean-Tobias Okala, the UN spokesman in Kinshasa.
"They were part of a coup attempt, and they will face justice in Congo"
Theophile Mbemba, Interior Minister
"We have almost 18,000 troops here to achieve our goal of peaceful and transparent elections," he added.
Mbemba said the group of 32 included three Americans, 10 Nigerians and 12 South Africans, adding that all the men had received visits from their respective ambassadors.
The South African ambassador said 19 of those arrested had South African papers. It was not immediately possible to resolve the discrepancy between that and Mbemba's figure of 12.
Ambassador Sisa Ngamane said that the country had sent identification papers to the authorities for those men and that it expected to be included in the investigation.
A statement released by the South African government said 16 of the South Africans worked for the Omega Security Company, while the remaining three worked as interpreters for a mining company.
Katya Thomas, the US embassy official, declined to comment. Nigerian embassy officials in Congo were not immediately available.