"Sweden will act for a new asylum system in the EU that is based on equal distribution and in which asylum is sought in the EU, not in the individual country," said Stefan Löfven in his speech.
Sweden has taken the second-highest number of asylum applications per capita in the EU, just behind Hungary, on 1,667 per 100,000 population. The Swedish government has been pushing for other EU member states to take in more refugees.
Löfven added he does not see how those who do not participate in asylum cooperation could participate in the union's visa free Schengen Area.
"Quite simply, if we are to share an external border and have free movement between our countries, we must also share a system of asylum reception," Löfven said.
Some EU countries have been restricting free movement in an attempt to limit the amount of people coming over their borders, and the Schengen system, a cornerstone of the EU, has been under threat.
The Social Democrat prime minister was positive about the recent agreement with Turkey, but this was criticised by some MEPs, with Sweden's Cecilia Wikström (Liberal Party) saying that people will find a way around Turkey's border controls, and Malin Björk of the Left Party saying that Sweden should not be held back in its work for asylum cooperation by countries like Hungary.
The Sweden Democrats blamed Sweden for having damaged the EU, and its MEP Kristina Winberg said that "the EU is standing before a political, humanitarian and social chaos."
Löfven: 'dangerous journeys across Mediterranean must stop'2:03 min 2:03 min
Swedish PM urges dialogue with Turkey0:48 min 0:48 min