Playing down talk about possible coalition options, Deputy Prime Minister Carmen Calvo said on Monday the Socialists would try to govern alone, while party officials said there was no hurry to decide.
Several sources in the party described the general mood as one of confidence that it could form a government.
"The Socialists will try to govern on their own," Calvo said in an interview with Cadena Ser radio. "We have more than enough (votes) to steer this ship along the course it must follow."
Jose Luis Abalos, a high-ranking Socialist, said after a strategy meeting that the party would "talk to all the groups and try to come to agreements" but that it was not desperate. "There will be those willing to cooperate," he said.
Prime Minister Pedro Sanchez's centre-left party celebrated into the small hours after increasing the number of seats it holds to 123 in Sunday's poll from 84 in the outgoing parliament.
It has been ruling in minority, passing legislation with support from hard-left Podemos and small regional parties.
If Sanchez (47) does seek a coalition partner, he could opt for a tricky alliance with Podemos that would probably require support from at least one Catalan separatist lawmaker. The alternative is to join forces with centre-right Ciudadanos, which risks upsetting his grassroots supporters.
Any coalition talks could take weeks or months, especially as parties talk tough to please their voter bases ahead of regional, local and European Parliament elections on May 26.
One of Ciudadanos' leaders, Ines Arrimadas, on Monday ruled out any pact or talks with the Socialists, saying her party was focused on the regional elections.
Any prolonged period of uncertainty in Europe's fifth largest economy is likely to exacerbate the continent's problems as it wrestles with the complexities of Brexit and other challenges.
For many observers, the Podemos option appears Sanchez's likelier path, even though the two parties are 11 seats short of a majority. Podemos leader Pablo Iglesias said he would happily enter a coalition and unions called on workers to take to the streets on May 1 to demand a leftist government for Spain.
"The chances of (Sanchez) getting a government (with Podemos are) at 90 percent, or better, but the chances of him passing the budget are 40:60," said Javier Diaz-Gimenez, economics professor at business school IESE.
CATALAN CHALICE
Vox, the first far-right political party to secure a significant presence in parliament since dictator Francisco Franco died in 1975, splintered the right-wing vote to leave the mainstream conservative People's Party (PP) with just 66 seats, its worst result since the early 1980s.
The PP, along with the Socialists, had dominated the political landscape since Franco's death.
Vox won 24 seats, fewer than expected, somewhat allaying concerns at home and abroad about the rise of the far-right. Support for nationalist and populist parties has surged across Europe in recent years.
Sanchez took office last June after the then-governing PP lost a confidence vote. He called Sunday's election when his budget failed to get through parliament after Catalan separatists refused to back it.
If Sanchez allies with Podemos, he would probably also need to cut another deal with the Catalans to secure a majority.
While Sanchez has ruled out any negotiations on Catalan independence, any deal with the separatists would rake over the coals of the most divisive topic of an often tense election campaign that was dominated by issues of national identity.
Under Spanish electoral law, a new government has two chances to be confirmed by parliament.
The first round requires a full majority, which it is likely to fail. But in any second round, a simple majority will suffice, which the Socialists and Podemos could achieve with backing of all regional parties except the Catalans, plus one abstention.
The separatist lawmakers are at the sharp end of Catalonia's independence drive, and precipitated a constitutional crisis in 2017 by unilaterally declaring independence after a referendum that authorities had banned. Several are on trial for sedition.
The pro-independence movement saw its negotiating power boosted on Sunday as its lawmakers won 22 seats.
"The ERC (main separatist party) will not want another election right now, so they will let (Sanchez) govern by abstaining," said ISES's Diaz-Gimenez.
CIUDADANOS AS BACK-UP?
Sanchez might instead try to clinch a agreement with Ciudadanos, which would give him an absolute majority.
He has not ruled out that option, though it appeared less likely after Ciudadanos leader Albert Rivera repeated after the election that he would be in the opposition.
Such a tie-up, though favoured by many in the markets, would also risk alienating many of the Socialists' core supporters.
Spanish stocks outperformed European peers to end 0.5 percent higher on Monday, the first time they had closed up after an election, while Spanish bond yields dipped.
