Scottish independence supporters marching through Glasgow were confronted by men giving Nazi salutes and waving Union Flags.

Police estimated 35,000 took part in the All Under One Banner event which began in Kelvingrove Park and ended at Glasgow Green.

When marchers walked along Clyde Street a group of men emerged and began hurling abuse. One man repeatedly gave a Nazi salute as another waved a Union Flag. Police are investigating.

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One independence supporter, who asked not to be named, filmed the altercation. He said: “There was about eight of them, shouting abuse and squaring up to the crowd. A couple of them gave Nazi salutes. They were looking for a square go. Police officers held them back.”

SNP MSP Stuart McMillan later tweeted about a separate incident on the corner of Renfield Street and Argyle Street.

He said: “On the Indi march and just had a Nazi salute and the middle finger from your supporters @scotlandinunion.”

Scotland in Union is described on its website as “a non-party not for profit group which unites people around a positive view of Scotland in the UK”.

When asked about the incident he witnessed, McMillan said: “There were a group of pro-union protestors. I saw two police officers and one of them was facing the pro-union protestors when it [the Nazi salute] was made. It was approximately 1.10pm.”

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A spokesman for Scotland in Union said of McMillan’s tweet about the organisation: “These disgusting smears are becoming more and more desperate from prominent nationalists who should know better.”

A spokeswoman for Police Scotland said there were no arrests at the march which they said attracted 35,000 people. The spokeswoman added: “We are aware of this picture online and we’ll look into this matter.”