Until recently, it appeared that the Spanish indignados movement had fizzled out. But on Sunday evening, a fledgling party born from its ashes proved otherwise, winning five seats and 1.2 million votes in Spain's European elections.

Barely 100 days old, and lead by Pablo Iglesias, a 35-year-old political science professor with a ponytail, Podemos (We Can) emerged as the third largest political force in many Spanish regions, including Madrid.

The idea behind the party is simple, Iglesias told the Guardian on Tuesday. "It's citizens doing politics. If the citizens don't get involved in politics, others will. And that opens the door to them robbing you of democracy, your rights and your wallet."

The soft-spoken, former Communist Youth party member may have stunned analysts with his party's performance, but it was not enough for him. The ruling People's party (PP) had won the elections, meaning that high unemployment and home evictions would continue, he said. "We want to build a political majority that reflects the social majority of Spain."

Podemos' lofty list of election promises includes doing away with tax havens, establishing a guaranteed minimum income and lowering the retirement age to 60. The party ran its European elections campaign on a shoestring budget, using crowdfunding and Iglesias' ubiquitous presence as a talking head on Spanish television to build momentum.

Voted in by Spaniards tired with persistent unemployment, austerity measures and corruption scandals, Iglesias said Podemos MEPs would act accordingly. Rather than the standard salary of more than €8,000 (£6,500) a month, "not one of our MEPs will earn more than €1,930, an amount that's three times the minimum wage in Spain". The remainder would either go to the party or a chosen cause.

"We're not going to travel to Brussels in business class. If any lobby group approaches us, we'll make that information public." One of his first items of business, Iglesias said, would be to propose that other MEPs do the same.

Podemos' success has had many in Spanish media asking questions about Spain's two dominant political parties. The PP and the Socialists together received less than 50% of the vote, a far cry from the 81% support they received in 2009. The top PP candidate, Miguel Arias Cañete, celebrated his victory in the elections, but acknowledged the results were a "serious warning" from voters.

The Socialists went further their worst election result. Leader Alfredo Pérez Rubalcaba announced on Monday he was stepping down, adding: "It's clear that we haven't regained voters' confidence." The party will hold a meeting in late July to choose new leadership.

The fertile ground for Podemos' rapid growth was laid by the indignados movement not the Socialists, said Iñigo Errejón, the new party's 30-year-old campaign director. While the movement was incredibly expansive and impossible to fully capture in a political party, he said, "many of us were there, in the plazas and in the protests, we listened to what people were saying and we took notes. Without the changes that the movement brought about in the Spanish political scene, Podemos wouldn't be possible."

The challenge for Podemos now lies in finding a balance between a grassroots movement, whose agenda depends on hundreds of working groups across the country, and a functioning political party. It has no leadership which can inform on day-to-day decisions and no system in place to hold its MEPs to account. "We're a citizen force, made up of people who got together and ran an electoral campaign practically without any money," said Errejón.

Their model right now is more focused on what they don't want to be. "Many political parties are always looking inside, never outside," said Errejón. "We don't want to structure ourselves in the same closed off way." As an example, he pointed to the Podemos' primaries for the European elections, which were open to anyone who wanted to participate and attracted 33,000 voters.

The next few months will determine whether Podemos can translate their success into a genuine shift in the Spanish political landscape, said Errejón, and quell those who call them a populist movement or one fuelled by protest votes.

The ultimate goal, he said, is bigger than just winning seats. "We don't just want to be part of a political system that is decomposing. Spain isn't lacking political parties. But what's missing is citizens engaging in politics. And we want be a tool for that."