According to the press release circulated by the party, the unsanctioned march along Vilnius' central Gedimino Avenue on the Day of Restoration of Independence "once and for all removed the alleged democratic veil off the young people who describe themselves as 'patriotic'."
The Social Democrats said individuals who support democracy should conform to decisions of democratic institutions, and disregard of such decisions may be considered anti-Constitutional.
"Regardless of the fact that the march was described as a stroll of free citizens in the city on a holiday, it was indeed a well-organized march of a few thousand people carrying posters and chanting pseudopatriotic chants. Pictures published in the media contained slogans, such as 'White Power', i.e., a racist group operating in the US that promotes the killing of blacks," reads the press release.
"March 11 is a celebration for all citizens of Lithuania, regardless of their ethnic, racial, or religious background. Patriotic feelings are demonstrated by a person's respect for the country's Constitution, fellow citizens and creation of well-being for all," the Social Democrats said.
The party said it urged citizens to stay alert and "responsible in their views of actions of far-right groups in order to avoid being deceived by their ideas, as the world has suffered from the atrocities caused by them on a number of occasions."
The controversial rally on Monday was an unsanctioned event, since Vilnius administration refused to issue a permit for the march along Gedimino Avenue, saying that the central street would host other events for the Day of Restoration of Independence.
About 3,000 people participated in the rally.
No major incidents were reported during the event, apart from a few drunk individuals detained by the police. The controversial slogans 'Lithuania to Lithuanians' were heard on a few occasions in the crowd.
On the day after the rally, Prime Minister Algirdas Butkevičius, the leader of the Social Democrats, said such events should not be feared, stressing the need to abide by the law.
"We should all abide by the existing laws in Lithuania. But I positively evaluate the fact that public order was ensured as proper preparations had been made. I believe we should not be afraid of marches but we should avoid certain chants, banners and maintain discipline. Every ban leads to major opposition," Butkevičius told journalists at the Seimas on Tuesday.