Honorary Patriarch Filaret, 90, called a rare news conference to accuse the young head of the newly created united church of governing single-handedly despite earlier agreements.
Ukraine is going through a sensitive transitional period after a comedian with no political experience, Volodymyr Zelensky, won a landslide victory in a presidential election last month.
For more than 300 years, Moscow controlled part of the Ukrainian Orthodox Church but Kiev this year won religious independence in a huge coup for the pro-Western authorities.
An enraged Russia called the move "catastrophic", charging it would have consequences for global Orthodoxy.
The charismatic Filaret had been widely tipped to become the head of the united church but Metropolitan Yepifaniy, 40, was chosen to the post last December.
Filaret, who in 1992 established the Ukrainian Orthodox Church of the Kiev Patriarchate independent of Moscow, claimed that Yepifaniy reneged on what he said had been agreements to lead the new church together.
"There was an agreement that I continue to govern the church in Ukraine together with Yepifaniy while he will represent the church abroad," he told reporters.
He claimed that Ukraine's outgoing president Petro Poroshenko was part of the agreement.
"We did not put it in writing because I trusted both the president and Yepifaniy. They lied to me," he added.
Filaret warned the infighting threatened the future of the country's independent church.
"In order to preserve the church, agreements have to be kept," he said, claiming that "anti-Ukranian forces" might be behind the latest tensions.
Filaret said that at first he tried to coach the young cleric but Metropolitan Yepifaniy refused to heed his advice and the two no longer spoke.
He claimed Yepifaniy would not have been given the church leadership without his support.
President-elect Zelensky had promised him not to interfere in religious affairs, he added.
'Thirst for power'
Yepifaniy's spokespeople did not immediately comment on the claims but the church leader rejected talk of a possible split Tuesday.
"We should jointly build the future in the united Ukrainian Orthodox Church," Yepifaniy said in an apparent attempt to paper over the tensions.
Many accused Filaret of clinging to power.
On Tuesday, a pro-Western political party issued a statement in support of Yepifaniy.
"We must say a resolute 'no' to all attempts to destabilise the Orthodox Church," the People's Front party said.
Political analyst Volodymyr Fesenko said he was saddened to see the veteran cleric's "escapade".
"This man has such a thirst for power," Fesenko said on Facebook.
Some suggested the uproar would play into Moscow's hands.
"Moscow is directly interested in such a development," religious scholar Yuriy Chornomorets told AFP.
But others said a majority of Ukrainians embraced the unified church and it would withstand the tensions.
"Ukraine's Orthodox Church will continue to exist the way it exists now," said religious scholar Viktor Yelenskyi.
Until recently the Ukrainian Orthodox Church was divided into three branches: one whose clerics pledged loyalty to Moscow; one loyal to Kiev and overseen by Filaret; and the smaller Ukrainian Orthodox Autocephalous Church.
But early this year the Istanbul-based Ecumenical Patriarchate of Constantinople recognised Kiev's religious independence, allowing for the creation of a unified Ukrainian Church.
The decision was taken after Russia annexed Crimea in 2014 and backed separatists who carved out two unrecognised breakaway regions in Ukraine's east in a conflict that has claimed some 13,000 lives.