The Argentina Football Association (AFA) have made a formal complaint to FIFA's Disciplinary Committee following the incidents during Wednesday's 2-1 loss to Morocco in their opening match of the Olympics.
A pitch invasion by Moroccan fans after Argentina's Cristian Medina had scored deep in stoppage time triggered a two-hour delay as the game in Saint-Étienne was eventually completed in an empty stadium.
Bottles, cups and firecrackers were thrown at Argentinian players during their goal celebration.
AFA said in a statement that it had lodged a complaint to FIFA demanding the "necessary regulatory measures be taken for an event of such seriousness."
The statement added: "It is imperative to guarantee the safety of the protagonists for the peaceful development of this beautiful sport that is football and from the home of Argentine Football, we will do what is necessary to make this happen."
Later on Thursday, FIFA said it had opened an investigation and appointed a security expert "to support the necessary investigations into the potential breaches of the FIFA regulations following the incidents that took place during the match."
Paris Olympics organisers said Thursday they would boost security at the Games and ensure security staff are available and well trained after the pitch invasion.
Organisers said the incident had not posed a major security risk and that lessons would be learned.
"We do not minimise the events of yesterday," Olympics security director Bruno Le Ray told reporters, adding that additional staff and crowd barriers would be brought in for upcoming matches at Saint-Etienne, where access to the pitch is easier than at other stadiums.
Le Ray said that on average 17,000 agents would secure some 40 competition sites and some 100 non-competitive sites such as the Olympic Village, training facilities and hotels.
On the busiest days, this would increase to 22,000 staff. Staffing levels depend on the sports, with more than 1,000 agents deployed for major team sports events, but a fraction of that for individual sports like athletics.
Argentina's team was left perplexed when, after play resumed almost two hours later, the referee ruled Medina's equaliser for offside after review.
Argentina coach Javier Mascherano described the events as "the biggest circus I've ever seen in my life."
Argentina senior captain Lionel Messi, who is not part of the Olympic squad, posted on Instagram an emoticon of a face with wide open eyes and the word: "Unusual."
AFA president Claudio 'Chiqui' Tapia has demanded for those responsible for the incidents to be punished.
"It was regrettable what we had to experience today as Argentinians in Saint-Étienne," Tapia wrote on social media. "Waiting almost two hours in the locker room, only for our players to have to go back out to warm up and continue playing a match that should have been suspended by the referee after the pitch invasion by Moroccan spectators and the violence suffered by the Argentine delegation, is truly senseless and goes against the competition rules.
"Furthermore, the opinions of the captains of both teams, who believed the game should not have resumed, were not heard.
"From the Argentine Football Association, we have already submitted the complaint to FIFA's Disciplinary Committee so that the relevant regulatory measures can be taken and a sanction imposed on those responsible."
Argentina are back in action against Iraq in Saturday's Group G game.
Information from Reuters contributed to this report.