At least 100,000 people have poured into the streets of Madrid in a huge show of support for Spain's new anti-austerity party.

The wave of popularity enoyed by Podemus on Saturday followed the electoral success of its Greek hard-left ally, Syriza.

A sea of demonstrators chanted "Yes we can!" and carried signs reading "The change is now" as they made their way from city hall to the central Puerta del Sol square.

Many in the crowd also waved Greek flags and the red and white of Syriza, an equally radical party whose stunning win at the polls last week has buoyed Podemos and its anti-establishment message.

"The wind of change is starting to blow in Europe," party leader Pablo Iglesias, a pony-tailed former university professor, said in Greek and Spanish as he addressed supporters.

"We dream but we take our dream seriously. More has been done in Greece in six days than many governments did in years," the 36-year-old said.

Syriza beat mainstream Greek parties with vows to end painful austerity measures and corruption and Podemos hopes to emulate its success with a similar message in Spain's general election in November.

Organisers put the turnout in Madrid at 300,000 while police said about 100,000 people had massed in the Spanish capital.

Podemos, which means "We Can", was formed only a year ago but the upstart party shook up the political scene in May by winning five seats in elections for the European Parliament.

Born out of the Indignants protest movement that filled Spanish squares in 2011 with demands for change, Podemos says it wants to prevent profitable companies firing workers, promote fully state-controlled healthcare and enact a "significant" minimum-wage hike.