MOSCOW (Reuters) - The head of the Council of Europe demanded on Wednesday that Russia allow gay rallies, weighing in on what has become an increasingly divisive issue since Vladimir Putin returned to the presidency.

As support for same-sex marriage increases in the West, Russia's gays say they face shrinking freedoms and rising violence, and Russian lawmakers are considering a law that would ban gay "propaganda" around minors.

Activists and rights groups say the loose wording of the law could be used to clamp down on demonstrations by lesbian, gay, bisexual and transgender (LGBT) people such as gay pride parades.

"Authorities have an obligation also to (ensure) that LGBT people can express their views and (hold) demonstrations," said Thorbjorn Jagland, secretary-general of the Council of Europe, of which Russia is a signatory.

"This is a fundamental principle in the European Convention on Human Rights," he said.

An aggressive crowd shouted insults and threw smoke bombs over police barriers to break up a gay rally last week in St. Petersburg, forcing activists to escape in minibuses only minutes after the start of the demonstration.

Moscow authorities also rejected two requests this week by LGBT activists to hold rallies, agencies reported, though activists say they will carry out a demonstration in a central Moscow park on Saturday regardless of the city's decision to ban it.

Attitudes towards gay people in Russia and former Soviet states are largely shaped by repressive Stalin-era policies, when sodomy was punishable by up to five years in jail.

President Vladimir Putin, who is looking to boost his support among conservative voters, has given the Orthodox Church a more public role as a moral authority as Russia experiences a religious revival since the fall of Communism.

Russian Orthodox church leader Patriarch Kirill told Jagland on Tuesday that his Church must remind people that homosexuality is a "sin before God".

While the number of documented cases of violence against gays in Russia is low, rights group Sova, which tracks extremist violence, says attacks on gays rose sharply after discussion of the nationwide ban.

A 23-year-old man in the southern city of Volgograd was tortured and killed after revealing he was gay.

(Reporting by Thomas Grove; Editing by Jon Hemming)