OAXACA, Mexico, Nov 7 (Reuters) - About 20,000 people marched in the Mexican city of Oaxaca on Tuesday to back a beleaguered state governor a day after guerrillas demanding he step down exploded bombs in the capital.

Demonstrators wearing white T-shirts filled an avenue on the edge of Oaxaca, chanting slogans in support of state Gov. Ulises Ruiz, who critics call corrupt and authoritarian.

"Ulises is the only governor who has worked for Oaxaca. We voted for him and he should stay," said fruit trader Jose Rodriguez, whose business has struggled since protesters took over large parts of the city in June.

Anti-Ruiz activists, who for months guarded barricades on Oaxaca city's streets, have failed to unseat him. The conflict has led to the deaths of more than a dozen people, most of them activists.

On Monday, simultaneous bomb attacks in Mexico City damaged the headquarters of Ruiz's Institutional Revolutionary Party, an electoral court and a foreign bank branch. Several small guerrilla groups claimed responsibility for the blasts.

Federal riot police armed with clubs and water canons have taken back much of the city after fierce street battles.

They now stand behind plastic shields and rolls of razor-wire in the graceful central plaza although police are absent from poor neighborhoods where support for protesters is strong.

Interior Minister Carlos Abascal, who for months failed to negotiate an end to protests, urged Ruiz on Tuesday to either strike a deal or temporarily step down.

Some pro-Ruiz marchers accepted there was corruption in the government. "Ulises has made some bad choices in his cabinet, but there is still time to correct the mistakes," said lawyer Jaime Cuello.

Ruiz could govern for four more years if he survives.