They were faced with a group of around 45 opponents, who launched a counter demonstration as the parade made its way through the city.
A Police Scotland spokeswoman said there were no arrests and the event passed off peacefully.
Organisers of the march, which marked the killings of 14 civilians by the British Army in Northern Ireland in 1972, had originally wanted to walk from the West End, through the city centre, past the cenotaph and on to Glasgow Green, a route it had not previously taken.
But council bosses insisted they march east of the city - from Royston in the north of the city, via High Street on the city centre's eastern periphery, to Glasgow Green - over fears of disorder. Concerns had also been raised about music being played when passing churches in the city centre.
The counter-protest had been arranged by a militant Loyalist group called the Regimental Blues.