She has collected nearly 140,000 signatures on a petition urging the preservation of the unity of the 10.5 million-strong nation.
The suspension of four-party talks to form a government this month has fuelled media speculation about the possible break-up of the 177-year-old nation, which functions as the seat of the European Union's main institutions.
However, polls show most Belgians favour unity.
'Strong signal'
Elio de Rupo, francophone Socialist party leader, said: "It's a strong signal and we must take notice of such signals since it doesn't happen often."
Police estimated the number of protesters swelled to 35,000 as they marched from the Gare du Nord railway station in central Brussels to the Parc du Cinquantenaire near the EU headquarters.
Fifteen students from a Flemish nationalist group were briefly detained after trying to stage an illegal counter-demonstration in front of the royal palace, police said.
Yannel de Wouters, one Brussels resident taking part in the march, said: "...we have loads of problems with politicians ... we have come here to show we are all together and in solidarity..."
Politicians from richer, more populous Dutch-speaking Flanders in the north want more autonomy, while those from poorer, French-speaking Wallonia are defending the status quo.
Belgians on either side of the language divide have their own schools and news media and different political parties.
The last time Belgium faced a problem on this scale was in 1988, when it took 148 days to form a government. The current 161-day crisis breaks that record.