The party, led since 2014 by telegenic former university professor Pedro Sanchez, came in second in last weekend's election, winning 22 percent of the vote and 90 seats in the 350-seat parliament.
The Socialists lost ground to far-left Podemos, which was founded just two years ago and came in a close third with 20.7 percent support garnering 69 seats.
Despite a result that ranks as their worst ever, the Socialists are in a position to decide if acting Prime Minister Mariano Rajoy's conservative Popular Party (PP) can stay in power.
The PP received the most votes of any party but it fell well short of an absolute majority in parliament, taking 123 seats, and will need the support of the Socialists to govern in a minority.
But Sanchez has said the Socialists will not support any effort by Rajoy to stay on in his post via a coalition or a minority government.
"We will vote against the continuity of the Popular Party at the helm of the government, with Mariano Rajoy as prime minister," he said Wednesday after holding talks with Rajoy.
Analysts said allowing the PP to stay in power could alienate left-wing voters who oppose austerity measures introduced by Rajoy in response to Spain's financial crisis.
"It would be political suicide," said Anton Losada, political science professor at the University of Santiago de Compostela in northwestern Spain.
He recalled that the Socialists focused their campaign on the need to "send Rajoy home".
Forming a pact with the PP could see the Socialists suffer the same fate as its Greek counterpart Pasok, which saw its support plunge after it joined a coalition led by the conservative New Democracy in 2012.
"If they pact with the PP it would be very complicated" for Sanchez because "the base of parties is always more radical" then its leadership, said Narciso Michavila, who heads GAD3 polling firm.
With left-wing parties holding the balance of power in the new parliament, Sanchez said the Socialists would try to form a government themselves by joining forces with Podemos and other smaller regional nationalist parties.
That outcome would mirror recent events in neighbouring Portugal where the ruling conservatives won an October election but fell to a Socialist government backed by leftist parties just days later.
But analysts warned that teaming up with Podemos also has its risks. Podemos is the only national party to back an independence referendum in the wealthy northeastern region of Catalonia, where secessionist parties have
an absolute majority in the regional parliament.
It has said support for such a referendum is "indispensible" for any deal with another party.
If Sanchez accepts this condition, he faces the wrath of Socialist party barons who are fiercely opposed to Catalonia's separatist drive, such as Susana Diaz, the head of the regional government of the southern region of
Andalusia, a Socialist bastion.
"We can't negotiate with those that propose breaking up Spain," she said during an interview broadcast Friday on radio Cadena Ser.
Podemos's demand on the Catalonia referendum was "specially designed to sink Pedro Sanchez" because if he agrees it would lead to the "collapse of the Socialists in Andalusia", Michavila said.
King Felipe VI is responsible for nominating a prime minister after the new Parliament convenes on January 13.
If no party leader manages to be approved by lawmakers as prime minister within two months of a first vote of confidence, fresh elections will have to be called.
Podemos, which has shown no rush to discuss a coalition with Sanchez, could surpass the Socialists if another election is held and become the main opposition party, said political analyst Josep Ramoneda.
"If Podemos sees victory is at hand, it will resist as long as possible to go to new elections," he said.