The “March for Change” is one of Podemos’ first outdoor mass rallies, as it looks to build on the recent victory of its close allies Syriza in Greece.
Podemos leader Pablo Iglesias told the crowd a “wind of change” was starting to blow through Europe.
The party has surged ahead in opinion polls, and has vowed to write off part of Spain’s debt if it comes to power.
Several of Madrid’s main avenues became a sea of people and purple, the party’s color, after its supporters travelled from all over Spain.
Marching from Madrid city hall to the central Puerta del Sol square, protesters shouted “Si, Podemos!”, meaning “Yes, we can”.
Broadcaster TVE reported that hundreds of thousands were at the demonstration, but there was no official tally.
“The wind of change is starting to blow in Europe,” Pablo Iglesias said, addressing supporters in Greek and Spanish at the start of the rally.
“We dream but we take our dream seriously. More has been done in Greece in six days than many governments did in years.”
Protesters are parading in the same streets that over the past six years have seen many other gatherings against financial crisis cutbacks imposed by successive governments.
Speaking in Barcelona, Spanish PM Mariano Rajoy said Podemos had no chance of winning elections.
“I don’t accept the gloomy Spain which some want to portray because they think that by doing so they will replace those who are governing and have had to face the most difficult crisis in decades. They will not succeed,” he said.
Many Spaniards are enraged over reports of political corruption and public spending cuts implemented by Mariano Rajoy’s People’s Party and before that by the Socialists.
The two big traditional parties have described the party – less than a year old and whose names translates as “we can” – as populist.
Since Podemos stormed onto the political scene in last May’s European elections, it has moved from strength to strength with its uncompromising message against austerity and corruption.
Both left-wing and right-wing media have criticized Podemos, accusing it of having ties with Venezuela’s left-wing leaders and alleging financial misconduct by some of its senior members.
The party’s leaders have in response promised to publish their tax returns, with Pablo Iglesias remaining defiant.
“In the face of their hatred, we smile,” is one of his regular pronouncements, according to the AFP news agency. After the Syriza triumph in the Greek elections he said that “hope had been born”.
Spain has now officially come out of recession but nearly one in four workers remains unemployed.
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