* Little sign of unrest by late afternoon
* Youths have clashed with security almost every night
* Crown prince urges a "focus on what's positive" (Adds activist report of heavy police presence, quote)
By Alexander Dziadosz
MANAMA, April 21 (Reuters) - Protesters blocked several roads and police fired teargas at a school in Bahrain on Sunday, activists said, as the Gulf state staged a Formula One race promoted by the government as pure sport but seen by the opposition as a public relations stunt.
Scores of police cars and a couple of armoured vehicles stood along the highway from the capital Manama to the race circuit, where the Grand Prix, won by Formula One world champion Sebastian Vettel, took place without incident.
"The number of security in some areas is more than the number of protesters," Sayed Yousif al-Muhafda of the Bahrain Centre for Human Rights Muhafda told Reuters.
Witnesses at the Sakhir desert circuit, roughly 30 km (20 miles) southwest of the capital, said there was no sign of unrest in the immediate vicinity.
Asked for comment on the reported clashes, which included more of the near-nightly violence between police and youths in villages near the capital, an Interior Ministry official said only that everything was normal.
Protests in the Gulf Arab country - a key Western ally that hosts the U.S. Navy's Fifth Fleet - broke out in 2011, with the Shi'ite-led opposition drawing thousands of demonstrators demanding democratic reforms from the Sunni-led government.
The unrest forced the cancellation of that year's Formula One race and although the event went ahead in 2012, it was overshadowed by violent protests in the country.
Muhafda said several protests and clashes broke out during the day, including in the villages of Sanabis, Al Daih and Jedhafs, where he said police arrested 13 protesters.
Some protesters had blocked several roads around Manama and police fired teargas at a secondary school in the city where students had been demonstrating, he said.
But a heavy security presence - especially in villages near the Sakhir circuit - made it hard for protesters to stage demonstrations for very long, and many of them were dispersed within about 10 minutes, he said.
Except for a black plume of smoke rising from a dirt field, there were few signs of unrest by late afternoon in mostly Shi'ite villages near Manama visited by Reuters.
Police cars patrolled the graffiti-adorned village of Diraz, where clashes have taken place in the last few days.
In Saar village, riot police with teargas guns and white helmets riding in all-terrain vehicles cleared a road that had been blocked with palm tree trunks. A puff of what appeared to be teargas burst down the road. But there was no sign of fighting and the police left quickly after clearing the road.
Nearby streets were blocked with cinderblocks, a rubbish bin and sticks. People stood in doors of shops, swept the streets, rode bicycles and walked dogs nearby.
Bahrain's Crown Prince Salman al-Khalifa, who attended Sunday's race, dismissed the suggestion the government was using the race to paper over human rights abuses. Speaking on Saturday, he said more than 15,000 people visited the circuit on Friday and more were expected on Sunday.
CALM AT THE TRACKS
"What I would like to say is let's focus on what's positive, let's build upon the platform that we have, and let's celebrate this event with Bahrainis who are really passionate," he told reporters at the circuit.
Crown Prince Salman is a driving force behind talks between the government and main opposition groups aimed at breaking the political deadlock. He described the race as an opportunity to transcend national differences.
On Saturday, protests broke out in about 20 villages, activists said, with protesters throwing rocks at police, who responded with tear gas in many cases.
Reuters could not independently verify most of the reports, but witnessed clashes on Saturday and on Friday night in the Sanabis and Budaiya areas west of Manama.
Chief of Public Security Major-General Tariq Al Hassan said on Saturday his forces would deal firmly with any illegal activity, an interior ministry statement said.
The government denies carrying out arbitrary arrests and torture and says any reports of wrongdoing by its security forces are investigated.
At the race track, spectators enjoyed a carnival atmosphere, watching music and dance performances. The opposition has hoped to use the race, watched by millions around the world, to put the spotlight on its pro-democracy campaign.
The government has hoped to show unity and has portrayed the protesters as trying to undermine Bahrain's international image.