MOSCOW (Reuters) - Thousands of demonstrators marched in the Belarus capital Minsk and elsewhere on Sunday as weekly protests demanding the resignation of veteran President Alexander Lukashenko continued, prompting police to detain more than 300 people.

Belarus, a country of 9.5 million that Russia sees as a security buffer against NATO, has been rocked by mass protests since an Aug. 9 presidential election which Lukashenko said he won. His opponents claim the vote was rigged and want him to quit.

Most protesters marched in remote residential areas of the capital, clapping hands, shouting "long live Belarus" and waving white flags with a red stripe in the middle, a symbol of the opposition.

"This (protest) does work as it is impossible to rule the country when the majority does not accept you. With protests we are showing that we are the majority," said one of the protesters Alisa, 21.

Lukashenko, who has been in power for 26 years, has shrugged off the scale of protests, saying they are sponsored by the West, and shown little signs of willingness to start a dialogue with the opposition.

Military vehicles and water cannon were seen on Minsk streets on Sunday, while uniformed men, many in helmets, grabbed people in civilian clothes, a witness aid and videos posted on social media showed.

In Minsk alone, the police detained more than 300 people accused of "violating the law on mass events", Russia's TASS news agency quoted the Belarus interior ministry as saying.

Russian President Vladimir Putin has urged political forces in Belarus to try to resolve differences through dialogue, and also said the ex-Soviet republic, a close Moscow ally, was facing unprecedented meddling by external forces.

Russia's backing is seen as vital for Lukashenko's chances of staying in power and its statements are closely scrutinised for changes in tone or any sign that Moscow could be pushing for some kind of managed power transition.