By Aaron Ross

KINSHASA (Reuters) - Tens of thousands of Congolese demonstrators chanting anti-government slogans and waving opposition flags rallied in the capital on Sunday to demand President Joseph Kabila step down when his mandate ends in December.

Kabila, 45, who has been in power since his father was assassinated in 2001, is under pressure at home and from increasingly exasperated world powers to step aside and call an election to choose a successor.

The vote is due on Nov. 27 but Kabila's government has said logistical problems are likely to delay it and has not set a new date. The electoral commission started enrolling voters on Sunday, but has said the process would take more than a year.

Some Kabila supporters want a referendum scrapping term limits so he can run again, as many African leaders have already done, and opponents accuse him of trying to cling to power.

"If the electoral commission does not convene the electorate, that will be high treason," revered opposition leader Etienne Tshisekedi, 83, told Sunday's rally during a half-hour speech, drawing loud cheers from the audience.

Among the crowd, one protester waved a white cross with the words: "Adieu Kabila, RIP."

Tshisekedi, who returned to Congo last week after spending two years in Europe for unspecified medical treatment, was runner-up to Kabila in a 2011 election that observers said was marred by fraud.

Tshisekedi formed Congo's first organized opposition platform under long-time autocrat Mobutu Sese Seko in 1982 and his homecoming has energized an opposition that failed to mobilize more than a few thousand supporters in a series of protests over the last two years.

CONFLICT FEARS

Past opposition rallies have turned violent and authorities have arrested dozens of Kabila critics since last year, but Sunday's protest near parliament was peaceful. Riot police remained several blocks away.

Foreign donors fear political tensions could easily lead to armed conflict -- Congo's mix of ethnic strife and foreign interference driven by competition over its fabulous mineral wealth has bloodied it for two decades.

Despite growing discontent with the government, the opposition faces long odds. Kabila has used his dominance of state institutions to undercut rivals and he retains powerful allies.

Tens of thousands of Kabila supporters joined a demonstration calling for Kabila to stay on in Kinshasa on Friday, two days after Tshisekedi's return.

Another prominent opposition figure -- former provincial governor and millionaire businessman Moise Katumbi -- told Reuters on Sunday that aviation authorities had refused his plane authorization to land. A government spokesman denied that.

Katumbi left Congo in May and was sentenced the following month in absentia to three years in prison for real estate fraud, charges he denies.

At 51, Katumbi is seen by some opposition parties as a more credible candidate than Tshisekedi due to his youth and wealth.

(Writing by Tim Cocks; Editing by Helen Popper)