TBILISI (Reuters) - Thousands of Georgians led by Orthodox Christian clerics marked "Family Purity Day" on Friday, marching down the same central avenue in Tbilisi that has been the scene of some of the fiercest anti-government protests in the country's history.

The contrasting groups staging the marches - pro-Orthodox and conservative on one side and pro-European on the other - spotlight the deep divisions within Georgian society as it grapples with an unprecedented political crisis.

For over a month, thousands of protesters, many of them young people, have filled Tbilisi's streets on a near-nightly basis to voice their opposition to a draft law on "foreign agents" they condemn as authoritarian and Russian-inspired.

The United States and the European Union have repeatedly warned the ruling Georgian Dream party to drop the bill, which protesters fear will harm the South Caucasus country's bid to join the European Union.

Dozens of rallygoers have been arrested or hospitalised since mid-April after police deployed water cannon and fired tear gas canisters and stun grenades to disperse the crowds.

By contrast, Friday's march received the tacit support of Georgian Dream, whose leading members including Prime Minister Irakli Kobakhidze took part.

Declared an official government holiday this year, the "Day of Family Purity and Respect for Parents" celebrates what the Georgian Orthodox Church calls the country's "family values" of marriage between a man and a woman.

LGBTQ rights are a contentious topic in Georgia, a traditionally Orthodox Christian country of 3.7 million.

Georgian Dream introduced a bill in March that would ban sex changes and adoption by same-sex couples, among other restrictions, a move seen by opponents as an attempt to boost its popularity ahead of elections later this year.

The Church began marking "Family Purity Day" in 2014, one year after an LGBTQ rights rally in Tbilisi was violently dispersed by crowds led by priests and conservative groups. May 17 is commemorated in many countries as the International Day Against Homophobia, Biphobia and Transphobia.

On Friday, throngs of mostly families and elderly people paraded down Tbilisi's streets, brandishing Orthodox icons and Georgian flags.

Outside parliament, where just a few days ago protesters were led away by police, people queued for their turn to kiss a large icon held aloft by a priest clad in black robes.

"Today is a great day," said marcher Zviad Sekhniashvili, dressed in the traditional garb of Caucasian highlanders.

"Family is our fortress... That's why God created man and woman: to have a family, to have kids."

Other holidaymakers said they saw family as linked to the concept of the Georgian nation.

"Family is like a little state," a woman who gave her name as Mariam said. "If our family is good, it's good for the country."

(Reporting by Reuters in Tbilisi; Writing by Lucy Papachristou in London; Editing by Nick Macfie)