(Adds Carter Center comments throughout) By Alistair Thomson KINSHASA, Nov 1 (Reuters) - International monitors gave Congo's historic elections a broad thumbs-up on Wednesday but said the tally could be close and urged candidates and their supporters to respect the result and avoid further violence. Sunday's presidential run-off and provincial assembly polls passed off peacefully across most of the vast country despite fears of violence following street battles between soldiers loyal to the presidential candidates after the first round. "All of us, international and national observers, are all the more aware of our responsibilities as the vote could be closer, and we need to be careful there is no attempt by extremists to contest the results by violence," Philippe Morillon, head of the EU observer mission, told reporters. Joseph Kabila, who took over from his slain father in 2001, won 45 percent in a July vote, against 20 percent for Jean-Pierre Bemba, a former rebel and vice-president in a power-sharing government set up to end a 1998-2003 war. No numbers have yet been published from Sunday's run-off between the two and provisional results may take three weeks. Diplomats in the capital Kinshasa say the closer the vote, the more chance of violence by supporters of the loser. The electoral commission said on Tuesday false results being reported by some people risked raising tensions already high in the capital Kinshasa, where the private armies of Kabila and Bemba fought bloody battles in August, killing over 30. "The Carter Center believes clear, unequivocal public messages by political leaders calling for calm can have a significant influence on followers," the U.S.-based election monitor said in a post-election statement. "Such statements would be welcome now," added the organisation, set up by former U.S. President Jimmy Carter. The first round of voting exposed a deep divide between Kabila's native Swahili-speaking east and Bemba's Lingala-speaking west, which includes Kinshasa. The EU has around 1,300 troops in Kinshasa, backing the biggest U.N. peace force, but the EU mandate expires on Nov. 30. VIOLENCE Voting was rerun on Tuesday in the northern town of Bumba, where police shot dead two rioters who destroyed polling stations. Polling was due to be rerun on Thursday in Fataki, eastern Congo, where people burned polling stations and up to 25,000 ballots after a soldier killed two election workers. Observers also said police in the port town of Boma shot in the air on Tuesday at an electoral commission office to disperse a rioting crowd stirred up by rumours of election rigging. The groups criticised media on both sides for giving unfair coverage to their favoured candidate during campaigning. "In flagrant violation of Congolese law and agreements that have been signed, the country's main audiovisual media continued to help candidates exclusively and broadcast messages of hate and incitement to violence," the EU mission said in a preliminary report on Wednesday. The EU said Congo's High Media Authority ordered National Radio and Television of Congo to halt broadcasts for 48 hours from Wednesday morning to punish it for airing interviews with Kabila but not Bemba. But Morillon said EU observers had judged the vast majority of polling stations on voting day as good or very good. "All our observers thus agree to recognise that everything took place in an orderly manner," he said in a statement. "All the same, faced with the risk of furious mad people trying again to contest the results through violence, we call each of the presidential candidates to demonstrate their worthiness of that position by controlling their most extremist supporters, as they have promised to do," Morillon said. (Additional reporting by David Lewis and Alain Amontchi)