By Jeremy Laurence

SEOUL (Reuters) - Millions of South Koreans elect the mayor of Seoul on Wednesday in a crucial vote seen as barometer of support for the leading parties and presidential hopefuls ahead of next year's national elections.

Both of the main parties have been beset by internal strife and falling support rates this year, and have thrown all their resources at winning the race for the prestigious position of Seoul mayor as part of efforts to rebuild their image.

"With issues being focused on the central government like the parliamentary and presidential elections, this will act as a good predictor for the next elections," said Lee Nam-young of Sejong University in Seoul.

Next year, Asia's fourth largest economy will hold parliamentary and presidential polls in the same year for the first time in two decades. The votes are scheduled for April and December respectively.

Opinion polls show the ruling Grand National Party (GNP) and the opposition running neck-and-neck, both at the national level as well as in the race for Seoul mayor, a position held by conservatives for the past decade.

Liberal rule by the opposition at the national level would translate into a step back from the big-business friendly policy of the current administration, and a shift toward aiding struggling small businesses, as well as welfare initiatives.

In a bid to win Seoul, the GNP's ace-card Park Geun-hye has emerged from self-imposed political hibernation to stump for Seoul candidate Na Kyung-won, and to boost her own image as she readies for a second run at the presidency.

Park, 59, was criticized by party faithful for sitting on the sidelines during by-elections earlier this year, when the GNP suffered heavy defeats, and for her perceived reluctance to step up to help the GNP as it tried to rebuild.

The daughter of former dictator, Park Chung-hee, had been the clear favorite to win the presidency next year, but her three-year stranglehold over opinion polls was shattered last month by a politically obscure university professor, Ahn Cheol-soo.

Ahn, a popular software entrepreneur, stunned the GNP and the opposition alike when opinion polls showed him as the country's preferred choice for president, after he had indicated he may take a stab at running for Seoul mayor.

The media-shy Ahn withdrew from the Seoul contest, but has backed another independent candidate, lawyer-turned-activist Park Won-soon, who is representing a broad alliance of left-leaning opposition parties.

Ahn only decided at the last minute to come out and back the opposition's Park in the Seoul vote, signaling he may be interested in taking a prominent role in next year's national elections.

Like the GNP, the main opposition Democrat Party has been in turmoil after its candidate lost out in a primary ballot to field a single liberal candidate in Seoul.

But a victory for the independent Park would boost efforts to form an opposition alliance, which would increase the liberals' chances of ending the GNP's grip on power in parliament and at the Blue House.

The top job in the city of 10 million people, which accounts for one-fifth of South Korea's population, is one of the country's high profile political posts. Two incumbents have gone on to become head of state, including incumbent Lee Myung-bak.

(Editing by Yoko Nishikawa)

(This story was corrected in paragraph four to change time of presidential election)