Leandro Schclarek Molinari, one of the coordinators, tells Radio Sweden that asylum seekers are not here "because of tourism".
"Many have been living as undocumented migrants all their lives. That's inhumane. Every person has rights, not only citizens," says Schclarek Molinari.
Abbos Ahmadi is one of the asylum seekers taking part in the march. He left Afghanistan six years ago.
"We have problems in our home countries and that's why we come here. We want to tell everyone that we are trying to have a normal life, to live like everybody else here in Sweden and in Europe. No one chooses to leave their country just to come over here and hide for several years," says Ahmadi.
The protesters taking part in the Asylum March are calling for a more humane migration policy and they are against the Dublin System, which says that the EU country that an asylum seeker first arrives in is also responsible for dealing with their asylum application. Unauthorised entrants to the EU are also required to submit their fingerprints to a Europe-wide database.
The Dublin System has come under fire from migrants' rights group who say it impedes the civil rights and personal welfare of asylum seekers. "The Dublin System is inhumane. People come here because they have escaped from something and when they are sent around to different countries, they can never feel free or settled," says Helena Vesterlund.
There is a core group of around 30 people who have walked the entire Asylum March route between Malmö and Stockholm, covering around 20 kilometres per day.
There are undocumented migrants from around the world here, and Swedish-born people, too. Participants say that the atmosphere over the past month has been uplifting, with strangers cheering the marchers on and offering them food and drink.
Schclarek Molinari says that when he and his friends return to Malmö, they will continue their grass roots campaigns for asylum seekers' rights.