In results described as "frightening" by the Swedish Newspaper Publishers' Association, 60 percent of MPs want to make it possible for companies to sue newspapers, magazines and broadcasters for defamation.
The findings are the result of a survey of all members of parliament carried out by polling company Sifo. Of Sweden's 349 MPs, 227 responded to the questions.
PeO Wärring, deputy chairman of the Swedish Newspaper Publishers' Association, said that MPs "do not understand the importance of freedom of speech and freedom of the press for an open and democratic society."
77 percent of MPs replied that newspapers should be banned from publishing names and photos of crime suspects until they are convicted. 55 percent said sexist advertisements should be banned. Both these issues are currently covered by voluntary codes of practice, with Swedish newspapers rarely naming suspects and sexist adverts dealt with by an independent body.
59 percent said that police should be banned from leaking details of investigations to the media. Sweden's current freedom of speech laws mean they can usually speak to the media about investigations without fear of disciplinary action.
55 percent wanted a law to limit the rights of media to report on famous people. As with most of the other issues, support for restrictions had fallen since the survey was carried out last year, when the Social Democrats were in power. Then, 74 percent of MPs wanted restrictions.
55 percent of those asked this year said that damages in cases involving press freedom should be "raised substantially."
"Freedom of the press and freedom of expression have been won by the people through political struggle. Our politicians must not forget this, and should take their responsibility for the citizen's right to know," said PeO Wärring.