(CNN) -- The demonstrators have no clear leader. Many say Twitter posts and Facebook groups brought them to the streets of Mexico's capital and cities around the country.
With presidential elections less than six weeks away, they are protesting media coverage of the campaign and criticizing the candidate widely seen as the front-runner.
Local media reports have described it as "the Mexican Spring," drawing a comparison with massive protests pushing for political change in the Middle East.
The surge of student activism has drawn attention at a key time during campaigning in the politically polarized country, where security concerns and economic problems have been top issues for candidates vying for the presidency.
"It was about time that Mexico woke up, that it stopped watching television," said Leonardo Mata, a student at Mexico City's Metropolitan Autonomous University who joined thousands marching in the capital on Wednesday.
TV coverage of the campaign has drawn sharp criticism from some protesters, who argue that national broadcaster Televisa has provided more favorable coverage to Enrique Pena Nieto, the Institutional Revolutionary Party candidate who leads in polls.
Televisa's president appeared to acknowledge the protests in a Twitter post this week.
#yosoy132 ¿Hasta cuándo?
"At Televisa we value the youth and we listen to their opinions. We are always open to them," Grupo Televisa CEO Emilio Azcarraga Jean wrote.
It was about time that Mexico woke up, that it stopped watching television
Leonardo Mata, student at Metropolitan Autonomous University
Mexican Interior Minister Alejandro Poire alluded to the protests Thursday.
"I am convinced that having youth that are enthusiastic, proactive, participatory youth that are demanding of us is without a doubt, a fundamental activity of our democracy, and it is there, and today it is being expressed with great vigor," he said.
Leftist candidate Andres Manuel Lopez Obrador praised the protesters.
"They are touching on a fundamental theme that has to do with the pretension of dominating the country through the almost absolute control of the media," said Lopez Obrador, a former Mexico City mayor who frequently criticizes the country's political establishment. He never conceded after officials declared Felipe Calderon the winner of Mexico's election in 2006 and has been known to refer to himself as "the legitimate president of Mexico."
Lopez Obrador and other opponents have accused Pena Nieto of receiving preferential treatment from the media since before the campaign began. The candidate, who was governor of the state of Mexico from 2005 to 2011, has denied those accusations and said he respects the youth protests against him.
Pena Nieto said Thursday that a recent university event where protesters jeered at him was a "rich experience."
"It allowed me to see the interest there is among the youth to participate in this democratic process. How great that it is this way. It is a strength that we have built between all Mexicans," he said Thursday at a forum on security and justice
But Pena Nieto was less positive in comments to CNNMexico immediately after the May 11 event at the Iberoamerican University, where crowds booed and chanted "get out" at the candidate.
"They are not all genuine," Pena Nieto said. "But in the end the free space of the university must be respected and I am totally and absolutely respectful."
Officials from Pena Nieto's campaign quickly dismissed the protests at the event, saying the outbursts were not from students, but from outsiders dragged there by political operatives to cause commotion.
Three days later, a YouTube video featured 131 students flashing their university ID cards, saying "We are students from Ibero. ... Nobody forced us to do anything."
The 11-minute video went viral. It has been viewed more than 1 million times in the past 10 days.
Posts promoting protests throughout the country on social media in recent days have used it as a jumping off point, using the phrase "#YoSoy132" ("I am 132") on Twitter and Facebook.
Maria Elena Meneses, a professor who studies new technologies and information at Monterrey Tech, said the way the Ibero students' actions appeared to be triggering protests fueled by social media was "unprecedented" in Mexico.
"It is probably extreme to say that it is a Mexican Spring, alluding to (the protests) in North Africa, but nobody can dare to underestimate an action in which social networks were the catalyst for youth unrest," she wrote in an opinion column for CNNMexico.com this week.
Many students in Mexico City on Wednesday said they were excited about the success of the protest, which police said more than 15,000 people attended.
"I believe in the movement. I believe young people, we have great power in our hands. We have information and media that other groups do not have," said Paula Diaz, 23, a student at the National Autonomous University of Mexico. "It is my duty to be here, informing people. I think we can do something great."
Some said the group needs stronger organization in order to prosper.
"We have to make the transition from noise to words," said Maria Fernanda Galicia, 22, a student at the Iberoamerican University.
Protesters plan to meet Saturday in a part of Mexico City known as Tlatelolco to form a more specific strategy and draw up goals for what they say is a burgeoning movement.
"There is a spark, but if we leave it apathetically, it will dissolve," said Angel Rodriguez, 19, a student at a music school run by Mexico's City's cultural ministry.
The plaza where students say they are planning to meet this weekend has significant historical significance in Mexico.
It is the site where many student protesters were killed during a rally in 1968. Increased democracy and free expression were among their demands at the time.