Podemos made the announcement after the Socialists signed a deal with centrist party Ciudadanos, which Podemos's Inigo Errejon told a news conference “prevents the possibility of forming a pluralistic government of change”.
The support of the party is vital to Socialist leader Pedro Sanchez as he seeks enough backing from lawmakers to become prime minister when they vote for or against his programme for government next week.
This was now “doomed to failure” by the agreement, Errejon added.
Even with Podemos's support, he would still be short of the tally needed, which means Spain still has no government in sight nearly 10 weeks after the elections.
Earlier Wednesday, the Socialists' Senate spokesman Oscar Lopez described the agreement between them and Ciudadanos as “a first deal”, adding on Spanish radio, “there are way more groupings that can make (Sanchez's) investiture possible”.
Sanchez and Ciudadanos chief Albert Rivera shook hands to applause after signing the agreement, which centres on what a new government led by the Socialists would look like.
It includes proposals for major judicial reforms, including changing the constitution to modify rules governing lawmakers' immunity from prosecution, as demanded by Rivera in return for backing Sanchez.
It also puts forward social reforms such as bringing back Spain's prized universal healthcare system, which has suffered from major spending cuts over the past years of austerity.
Spain has been mired in political deadlock since December elections
resulted in a hung parliament split among four main parties, none of which has
enough seats to govern alone.
The ruling conservative Popular Party (PP) won the most seats but fell short of an absolute majority. The party's leader, acting prime minister Mariano Rajoy, gave up attempts to form a government after he failed to get support from other parties fed up with austerity and the corruption scandals plaguing his grouping.
King Felipe VI then asked runner-up Sanchez, whose Socialists won 89 seats out of 350, to form a government, but he too has struggled to form an alliance.
“It wasn't easy for the Socialist party and Ciudadanos — which have different projects — to be able to put what unites them… above what separates them,” Rivera told reporters.
Even with Ciudadanos, which won 40 seats, Sanchez still does not have enough votes and will therefore need the backing of other parties – a difficult task as all have conflicting agendas.
Anti-austerity party Podemos, an ally of Greece's ruling Syriza, won 65 seats and would therefore be a valuable partner.
But the long-established Socialists are wary of joining forces with an upstart party born just two years ago out of anger over austerity, and which ultimately seeks to supplant it.
The two parties are also deeply divided over Catalonia's independence movement.
Although it does not want to see Spain split, Podemos backs the idea of a Scotland-style referendum in the northeastern region. Sanchez, however, is resolutely against this.
And crucially, Podemos has previously refused to enter a government that would also include Ciudadanos, pushing instead for a left-wing coalition with its leader Pablo Iglesias as deputy prime minister.
The PP meanwhile has said it will vote against any government it does not lead.
Sanchez, therefore, faces an uphill struggle next week to win parliament's backing for his programme.
He needs an absolute majority – 176 ballots – in the first vote of confidence due to take place on March 2nd.
That is almost certain to fail, leading to another vote 48 hours later, in which he would only require a simple majority.
Failing that, the country could be forced to return to the polls by the summer.
As Spain emerges from a severe economic crisis, many say fresh elections would be a disaster for the country, particularly as opinion polls suggest the outcome of a new election would by and large be the same as that held in December.
On Tuesday, Spanish business leaders warned that going to the polls again would be an “incomprehensible failure.
By Marianne Barriaux / AFP