* Tens of thousands demand president resign
* Authorities cancel traditional military parade
* Influential Orthodox patriarch urges dialogue (Updates with march to cathedral, patriarch quotes)
TBILISI, May 26 (Reuters) - Tens of thousands of opposition supporters rallied in Georgia on Independence Day on Tuesday to demand the resignation of the president, whose government cancelled a military parade to avoid confrontation.
Protesters waving white ribbons packed the 60,000-capacity national football stadium, in what appeared to be the largest rally since the opposition launched daily demonstrations against President Mikheil Saakashvili six weeks ago.
The opposition accuses 41-year-old Saakashvili of monopolising power since the 2003 "Rose Revolution" that ousted the ex-Soviet old guard of Eduard Shevardnadze. He has come under renewed pressure since a disastrous war with neighbouring Russia in August last year.
The government last week called off a traditional military parade planned for Tuesday in Tbilisi to avoid a clash. Protest organisers led supporters in a march to the main Holy Trinity Cathedral instead of the parliament as originally planned.
The head of the influential Georgian Orthodox Church, Patriarch Ilia II, urged dialogue.
"It has become a rule in Georgia -- the first two presidents were ousted, and what did we get from that? Would it not be better to listen to each other, we should be able to listen to each other," he told the packed cathedral.
Georgia's first post-Soviet president, Zviad Gamsakhurdia, was ousted during a civil war in 1992.
Tensions are running high in the country of 4.5 million people on Russia's southern border, where Moscow and the West are competing for influence over oil and gas transit routes.
Brief clashes between police and protesters in early May, and a failed mutiny at a tank base outside Tbilisi the same week deepened fears of a wider anti-government rebellion.
Former Saakashvili ally Nino Burjanadze told the rally: "We will not take a single step back. All we demand is the president's resignation."
RISK OF VIOLENCE
Saakashvili has ruled out resigning. He marked Georgian Independence Day -- reinstated with independence from the Soviet Union in 1991 -- at Tbilisi's military cemetery.
"With one hand we fight to free our land from the occupiers, and with the other we build our country," he said in a speech.
The U.S. and European Union on Monday urged the government and opposition "to end the current stalemate on the streets and begin negotiations immediately and without preconditions on a new program of reforms to invigorate Georgia's democracy".
The government says it is offering reforms to provide a fairer distribution of power. The opposition says it has heard such promises before and wants Saakashvili to go.
Analysts questioned the appetite of the Georgian military to parade with full pomp, nine months after Russia crushed its assault on the breakaway pro-Russian region of South Ossetia.
Georgia lost what footholds it had in South Ossetia and the rebel Black Sea region of Abkhazia, both recognised by the Kremlin as independent states after the war.
A May 5 mutiny at a tank base outside Tbilisi cast doubt over the loyalty of the military and overshadowed NATO military exercises through May in Georgia, which have angered Russia.
But analysts question whether the opposition commands enough support, despite the impact of the global economic crisis.
The economy is forecast to contract 1 percent in 2009, down from growth of more than 12 percent in 2007 on the back of broad economic reform and foreign investment.
Diplomats warn the longer the stalemate drags on the greater the risk of violence.
Watched closely by its Western allies, Georgia is anxious not to repeat a 2007 crackdown by police firing rubber bullets against the last peaceful protests against Saakashvili. (Editing by Ralph Boulton) (Additional reporting by Niko Mchedlishvili)
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