0119 GMT March 30, 2020
The All Under One Banner (AUOB) march from the west end to Glasgow Green took place in very poor weather conditions, BBC reported.
The UK government has said it does not support a further vote on independence.
The "emergency" march was organized in the wake of last month's general election, which saw the pro-independence SNP win 48 of the 59 seats in Scotland while the Conservatives won a majority across the UK as a whole.
It is the first of eight marches that the grassroots AUOB group plans to hold across Scotland over the coming year as activists aim to increase the pressure for independence.
The organization has staged several similar marches and rallies in town and cities across Scotland over the past five years.
AUOB decided that the march would definitely go ahead despite the cancellation of the rally, with the group tweeting: "If we let some Scottish rain stop us marching then we've no chance. The march is on."
Neil Mackay, one of the event's organizers, said: "Organizing outdoor events in Scotland in winter is always difficult and is always subject to our weather.
Scottish voters backed remaining in the UK by 55% to 45% in a referendum in 2014 – but Nicola Sturgeon, the SNP leader and Scotland's first minister, says she wants to hold another vote on independence later this year.
That currently looks unlikely to happen because the UK government has made clear it will not transfer the powers that Sturgeon says would be needed to ensure any referendum is legal.
The first minister has ruled out holding an unofficial referendum, similar to the disputed one in Catalonia in 2017, as she does not believe it would lead to independence regardless of the result.
Another AUOB march will be held in Glasgow in May, with similar events scheduled for Arbroath, Peebles, Elgin, Kirkcaldy, Stirling, and Edinburgh.
The protests came the day after former Labour cabinet minister and MP Ben Bradshaw declared he was “100% certain” that Scotland would choose to leave the UK in the event of a second referendum on independence.
Bradshaw told German newspaper Der Tagesspiegel: “The political class in England – and this includes my own party – must very quickly recognize the Scots’ right to self-determination”, which was then retweeted approvingly by Sturgeon.