"We understand this request. The security of our citizens is an absolute priority. We join the authorities in proposing a delay and ask people not to come this Sunday," the organisers said in a statement today.
The authorities earlier asked for the march to be put off, perhaps for several weeks, to allow the police to concentrate their resources on the investigation into the attacks which left 31 dead and 300 wounded.
In an earlier statement, the organisers said the march planned for tomorrow was meant to show that Brussels and the country at large refused to be intimidated by terrorism and that everyone stood together.
"This week, we, Belgian citizens have been attacked, in how we live, our customs, our rights, our liberty," they said.
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"The first reaction in such events is to withdraw but on reflection, fear must give way to hope and the defence of our values."
The march was due to begin at 2:00 pm (1830 IST) at the central Place de La Bourse which, carpeted with flowers and tributes, has turned into a shrine to the victims.
"Let us allow the security services to do their work and that the march, which we too want to take part in, be delayed for several weeks," Mayeur told a press conference with Jambon at the national crisis centre.