"We don't know the kidnappers, but according to the information we have, this kidnapping was planned and carried out in collaboration with members of a self-defense group calling itself 'Revolution and Justice'," party spokesman Igor Berenger Lamaka told The Anadolu Agency.
Lamaka, whose party was part of the anti-balaka militia, noted that the "Revolution and Justice" group was active in Paoua, an area located some 600km west of Bangui.
He said the sports minister had been a leader of the group before being appointed to his current position, adding that a small anti-balaka group had been used to kidnap him.
"Our party has nothing to do with this small anti-balaka group," Lamaka said. "We also denounce the minister's kidnapping."
Soon after Sayo left the Galabadjia III Church on Sunday morning, he was kidnapped by gunmen, according to members of the minister's family.
His wife and brother were both present at the time of the abduction.
They said they could neither identify the kidnappers nor determine the location to which Sayo had been taken.
It was the fourth kidnapping to take place in CAR since last Monday. A French female civil society activist was kidnapped last week, along with a clergyman and a female worker from the local United Nations mission.
All three were eventually released.
The kidnappers demand the release of Rodrigue Ngaïbona, known locally as "Andjilo," from prison.
Ngaïbona was arrested recently by the UN mission on suspicions that he had been involved in the massacre of dozens of Muslims since December 2013.
CAR descended into anarchy in 2013 when Muslim seleka rebels removed President Francois Bozize, a Christian who had come to power in a 2003 coup. The rebels later installed Michel Djotodia, a Muslim, as interim president.
Djotodia stepped down last year to be replaced by a Christian leader amid a wave of sectarian violence.
Since then, the country has been plagued by tit-for-tat violence between Christian anti-balaka militiamen and former seleka fighters.
The 12,000-troop UN mission (MINUSCA) began deploying in the troubled central African country last year under a mandate from the UN Security Council.