Huge crowds of anti-austerity protesters swarmed the streets of Madrid on Saturday during a "March for Change" led by Spain's leftist party Podemos.

The demonstrators chanted "We want change," and "Yes we can," with many waving Greek and Spanish flags. A BBC correspondent in attendance described the march as having a "carnival atmosphere."

Although official tallies of how many people were at the demonstration have not been provided, Spanish state television provider TVE estimated that hundreds of thousands of people participated.

The demonstration is the biggest show of support for the Podemos party, whose popularity has rapidly surged in recent months. Although the party was only formed a year ago, it surprised many by winning five seats in the European Parliament in May.

Podemos, which translates to "we can," now leads in public opinion polls and is widely expected to dominate Spain's upcoming national elections this year. Leaders of the party promise to write off Spain's debt, if elected.

"We want change," Podemos leader Pablo Iglesias told the Associated Press. "I know that governing is difficult but those who have serious dreams can change things."

The rapid rise of Podemos and other similar parties in Europe, such as Greece's Syriza party, is indicative of the shifting attitudes regarding the continent's economic fate. Many in Spain and Greece are frustrated with the high levels of corruption and unemployment in their countries, and are looking beyond the two-party system and toward leftist policies for alternative solutions.

Supporters of Podemos say they are fed up with years of financial cutbacks and other harsh austerity measures that have been imposed on the country by the governing People's Party.

"It is the only way… to kick out all of those politicians who are taking everything from us," marcher Jose Maria Jacobo told Reuters. "They even try to take our dignity away from us. But that they won't take that from us."

Podemos is closely associated with the leftist Syriza party in Greece, which won elections last week. Newly elected Prime Minister Alexis Tsipras vowed to end the widely unpopular austerity measures imposed on Greece by foreign creditors, which he said caused "humiliation and suffering" throughout the country.

Although Spain is officially no longer in a recession, unemployment is still widespread in the country, where nearly one in four people are jobless. Last year was the first time that Spain saw economic growth since the country was pushed to the brink of financial collapse in 2008.