Ukraine's parliament on Thursday postponed a vote on a religious bill that has outraged Russia because it suggests imposing severe restrictions on the branch of the Orthodox Church headed by the Moscow patriarchate.
Russia is particularly concerned about the possible seizure of its churches in Ukraine.
Several thousand worshippers of the Moscow church staged a peaceful protest outside the parliament building in central Kiev ahead of the proposed vote.
The draft legislation assigns a special status to religious organisations whose leadership is based in an "aggressor state".
Kiev and its Western allies accuse Russia of plotting and backing a three-year war in the east of Ukraine that has claimed more than 10,000 lives. Moscow firmly denies the charge.
A member of Ukrainian President Petro Poroshenko's ruling party said lawmakers had failed to gather enough support to vote on the bill Thursday.
"Our faction decided that this legislation was not ready for consideration," Oleksiy Goncharenko told the Interfax-Ukraine news agency.
"For this reason, this bill will not be considered today."
It was not immediately clear when the draft legislation might be presented to parliament.
The bill suggested that the Moscow-based branch of the Ukrainian Orthodox Church be forced to renew its registration with authorities within a three-month period and be placed under supervision.
It said Russian-based churches that "systematically violate Ukrainian law" would be stripped of their registration and banned.
Russian Orthodox Church Patriarch Kirill warned this week that the proposed bill "threatens the constitutional rights of millions of Ukrainian believers".
In a statement, he added that it could also "cause a wave of violence and new seizures of churches, and escalate intercommunal conflict in Ukraine".
Kirill accused Ukraine of illegally seizing more than 40 Moscow patriarchate churches between 2014 and 2016 and warned that the proposed law would make their takeover permanent.
Ukraine is a predominantly Orthodox Christian country where most of the faithful are members of the Kiev-based branch of the church.
Followers of the Moscow patriarchate primarily live in the east while some people in the western and central regions belong to the Greek and Roman Catholic Churches.