Nikolay Alexeev, a gay rights activist, said the mayor of Strezhovoy had agreed to hold the march, which was scheduled for 24 July.
In a post on Russian social media site VK, Mr Alexeev said: “Strezhevoy may become the first town in Russia where the gay parade procession will take place with the approval of the authorities.”
He also posted a letter he said he received from town officials which approved the march but asked to change the route the activist had suggested.
However, he later said the mayor had got “cold feet” and turned down the parade, posting another letter from officials saying they were withdrawing permission on account of a law to protect children.
The letter cited a law to protect “children from information that may harm their health or development”.
It also said the event could be seen as LGBT+ propaganda and said the town may not be able to ensure the safety of participants.
Last year, another event which would have been Russia’s first-ever gay pride event was cancelled within 24 hours of its announcement.
Mr Alexeev said he had received permission to hold the rally in the village of Yablonevy, near the town of Novoulyanovsk, which has a population of seven people.
But local authorities later said the news was “not true” and stressed “we will not hold any gay parades”.
Applications for gay pride parades are regularly turned down in Russia, due to a law banning “homosexual propaganda”.
Mr Alexseev said he sent 378 requests to cities across Russia in an attempt to arrange the country’s first gay pride event.
He published the official refusals on his social media pages and said he plans to submit them to the European Court of Human Rights.