The ruling bloc rushed through the bill in late June in response to Vilnius Municipality's initiative to open a "pop-up" beach on the square in a move that some politicians regard as disrespect for the memory of freedom fighters.
Despite "many shortcomings", the president decided to sign it into law "in light of the current political context" so as "not to become embroiled in political intrigues" in the run-up to October's parliamentary election, his office said in a press release on Friday.
"I see many shortcomings in the process of passing the law," Nauseda said in the press release.
"Members of the general public, competent authorities and heritage protection experts were not involved in the drafting of the law," he said. "It was debated in the Seimas under the urgency procedure, which further limited possibilities for interested persons and institutions to submit their opinions and assessments".
According to the president, neither the Seimas nor other authorities can unilaterally make decisions on how to perpetuate historical memory which is "an integral part of the culture" and "a national value".
The law designates the capital's Lukiskes Square as the main representative square of the Lithuanian state with a monument to Vytis, its national emblem featuring a knight on horseback.
The law requires ensuring "public peace" and "due respect" for the memory of Lithuania's freedom fighters and the participants of the 1863–1864 uprising against Tsarist rule who were executed in the square in 1864.
The square must be used in a way that does not compromise public order or offend good morals, according to it.