Cosatu has been accused of meddling in Swaziland's affairs after it publicly declared its support for the People's United Democratic Movement.
It also called on other members of the pro-democracy movement to "show unity" and support the party.
The trade union federation's president, Sdumo Dlamini, made the appeal at a meeting of Swazi opposition parties in Johannesburg on August 18. It rattled the organisers, who had taken pains to give all participants an equal platform and create a space that does not exist in Swaziland, where political parties are not recognised.
Citing Pudemo's charter, the "people's manifesto", as a blueprint for the future of Swaziland, the Swazi-born Dlamini said the country's various progressive movements had to unite behind Pudemo. "Working together is what is going to be key for the people of Swaziland. We confuse people when they see different faces of the liberation struggle … Pudemo must continue to lead that struggle."
Sibongile Mazibuko, the fiery president of the Swaziland National Association of Teachers, reacted angrily to the comments, which upset the other five opposition parties attending the indaba.
"We have a problem with this," she said. "It is an insult for someone else from outside to tell Swazis what to do. Swazis must decide what they want for themselves. Cosatu has made no survey of Swazis to ask us if we want Pudemo to represent us.
"We have come very far and have created a constituent assembly made up of churches, non-governmental organisations, unions and other associations to fight for our democracy. It is only Pudemo which has refused to take part and now Cosatu is telling us they should lead us."
Mazibuko said Cosatu's declaration also potentially threatened the unity of the newly formed Trade Union Congress of Swaziland, which Cosatu backs. The trade union has been working closely with the Swaziland Democracy Campaign to organise the upcoming "global week of action" for the country.
"Many of my members are not part of Pudemo and do not wish to be part of Pudemo, but now has the trade union congress become a vehicle to promote Pudemo?" Mazibuko asked.
Referring to the recent teachers' strike that paralysed the country and led to King Mswati III calling a Sibaya (people's Parliament), Mazibuko said: "We, the teachers, have been mobilising people to support our calls for an end to this autocratic system of governance, but are you now telling me we have been doing this on behalf of Pudemo?
"This is simply people trying to grab personal glory and it undermines our cause."
Defending his president's comments, Cosatu's international relations secretary, Bongani Masuku, who is also a Swazi, told the Mail & Guardian: "Cosatu recognises Pudemo as a leading political force in Swaziland, just as the ANC was recognised as South Africa's leading force. We do not expect everyone to be happy about that."
Masuku, who refused to confirm whether he was a member of Pudemo, said the most important thing was that there is unity among progressives in Swaziland.
Pudemo, which has been banned in Swaziland under terrorism laws after several alleged bomb attacks, is campaigning for multiparty democracy.