A non-Olympic sport, orienteering, meanwhile raised the possibility of breaking with SportAccord and setting up a new organization for the federations.
Sheikh Ahmad Al-Fahad Al-Sabah, president of the Association of National Olympic Committees, said "it is time to put personal matters aside" and stand behind Bach's reform agenda "for the benefit and harmony of the Olympic movement."
The Kuwaiti sheikh issued a statement urging unity in the wake of Vizer's attacks on the International Olympic Committee. Nearly two dozen sports have suspended or withdrawn their membership in Vizer's SportAccord, which represents Olympic and non-Olympic federations.
Peruvian organizers have also pulled out of hosting Vizer's multi-sport World Combat Games in 2017.
Sheikh Ahmad and Vizer had been allies until the SportAccord leader challenged the IOC and sought to organize his own multi-sport games.
The sheikh's public statement marked another personal blow for Vizer, who has been left increasingly on his own since delivering a speech criticizing the IOC at the opening of the SportAccord convention in Sochi last month. Vizer called the IOC system "expired, outdated, wrong, unfair and not at all transparent" and said Bach's "Olympic Agenda 2020" reform program was of little use to the federations.
Sheikh Ahmad said Vizer's views "do not represent the view of ANOC and other Olympic movement stakeholders and ANOC is keeping its distance from them."
"The Olympic movement is strongest when it is united," he said. "There are many different stakeholders with the Olympic family but under the leadership of the IOC we must all collaborate in order to provide the best environment for our athletes."
Sheikh Ahmad also took a direct swipe at Vizer by saying he would like to know how SportAccord shares its income with international federations and how judo distributes money to the national bodies. Vizer is also president of the International Judo Federation.
Sheikh Ahmad's support for Bach comes as no surprise. The Kuwaiti, who is an IOC member and head of the Asian Olympic Council, was influential in building support for Bach's successful candidacy for the IOC presidency in 2013. He is also chairman of Olympic Solidarity, the IOC program which distributes revenues to national committees and athletes.
But the sheikh's intervention resonates symbolically, as he represents 205 national Olympic bodies and is considered arguably the second-most powerful official in the Olympic world.
While more than 20 Olympic sports have suspended or withdrawn their SportAccord membership, four non-Olympic federations have come out against Vizer in recent days — karate, korfball, motor sports and orienteering.
"I had hoped that, after the valid concerns of many federations were expressed in Sochi, wiser counsels may have prevailed but that does not appear to have been the case," international orienteering federation president Brian Porteous said in a letter to Vizer.
"Surely accord should be the primary objective of SportAccord, not as appears now to be the case, discord," he added.
Porteous said orienteering and other federations will want to resign from SportAccord if it does not represent their views, and suggested they could leave to form their own organization.
If SportAccord does not change, individual federations and Olympic and non-Olympic associations "may need to come together to establish an effective organization which can deliver and better reflect the views of its membership," Porteous wrote.
Sheikh Ahmad and Vizer have skirmished over the launch of a proposed World Beach Games. The two had previously agreed to work together on the project, but Vizer announced in Sochi that SportAccord would launch the event on its own in 2017.
Sheikh Ahmad said Tuesday he is pressing ahead with his own plans for the games.
"Under the leadership of the IOC, ANOC is co-operating and co-ordinating with other Olympic stakeholders for the new project of the Beach Games," he said. "The project will be launched very soon and will serve our athletes and bring benefits to the wider Olympic movement."