By Rory Carroll

SAN FRANCISCO, May 25 (Reuters) - California sold just 11 percent of the carbon emission permits it offered at auction last week, state environmental officials said on Wednesday, a surprisingly poor showing that reinforced criticism that the program has an oversupply of permits.

California and trading partner Quebec hold the quarterly auctions as part of their cap-and-trade program, which puts a price on carbon by requiring large emitters like manufacturers and oil refineries to either cut their output or obtain a steadily declining number of emissions permits.

California carbon allowances (CCAs) have been trading about 30 cents below the auction price floor of $12.73 per tonne in the secondary market for weeks, pressured by concerns about a lawsuit against the program and questions about its political support.

The California Chamber of Commerce filed the lawsuit in 2012, arguing that the auctions amount to an illegal tax. Earlier this year, an appeals court judge sent letters to lawyers on both sides with detailed questions about the case, shaking market confidence.

Some market sources had expected the state to sell at least half of its offering, and were surprised that it sold just 7.3 million of the 67.7 million permits covering 2016 emissions and 9 percent of the permits offered to cover 2019 emissions.

Since California only managed to only sell permits consigned to it by utility companies at the May auction, it will be required to hold back about 36 million state-owned permits until it conducts two consecutive sell-out auctions.

Market sources said the requirement, designed to remove excess supply from the market, should help bring demand back in the short term.

Mary Nichols, chair of market regulator the California Air Resources Board, said the goal of the cap-and-trade program was to reduce emissions, not sell permits. If allowances go unsold, that means reductions are occurring beyond the program's annual targets and the program is working, she said in a statement.

"Although the program, like all markets, is subject to some fluctuation, we remain on a steady low-carbon trajectory with a historic transition to more efficient and sustainable energy use," Nichols said.

The weak demand raises the prospect that California will not earn as much money from the sales as it had expected.

Money raised from the auctions goes into an account dedicated to funding low-carbon programs like California's high-speed rail project.

The state's failure to sell out of permits during its February auction and again at last week's auction raises the prospect that the Greenhouse Gas Reduction Fund, which was expected by the state to receive about $2 billion a year, could fall short.

(Reporting by Rory Carroll; Editing by Richard Chang)