The anti-immigration Sweden Democrats' put the bid to parliament on the same day that lawmakers in Paris voted in favour of a hotly contested measure to strip convicted terrorists of their French nationality.
But in Sweden, only the anti-migrant party's 45 lawmakers voted for the introduction of the amendment. Another 236 voted against, while 16 MPs from the Left Party abstained.
Meanwhile, Sweden's parliament adopted its new anti-terror law, which toughens existing legislation.
In a reference to jihadists linked to groups such as Isis going to war-torn Syria, the new law punishes those who travel abroad to join a terrorist group with two years in prison.
The law also stipulates those who undergo training to carry out a terrorist act must serve six years in jail, while those who finance a terrorist group must spend two years behind bars.
Those convicted of travelling to another country to seek training or to commit a terrorist act will also be handed two-year sentences.
Sweden's intelligence service Säpo has identified 292 people as having left Sweden since 2013 to join the Islamic State jihadist group, among them 133 who returned home.