In a vote on Wednesday, the line pushed through in the Parliament's Committee on Civil Liberties and Rights (Libe) won with 384 votes in favor to 237 against.
The result is a victory for the right and far right in parliament, while large parts of the parties on the left are deeply critical of the proposed new rules.
The rules include which countries are considered so safe that people can be sent back there, instead of having their applications processed in the EU.
EU member states have also recently chosen a similar line in their handling of the issue.
