Sanchez said on Wednesday he would step back "for a few days" to decide whether he wants to continue leading the government after a court launched a business corruption probe into his wife's private dealings.
He said this was part of a sustained campaign of slander against him and his family by political opponents.
Sanchez denied the allegations made against his wife, Begona Gomez, and said he would announce his decision on his future on Monday.
"Prime Minister, stay, Pedro, stay - we are with you," Maria Jesus Montero, Deputy Prime Minister and Treasury Minister, told a meeting of the federal committee of the Socialist Party at its Madrid headquarters on Saturday.
Outside, euphoric supporters thronged the streets and played popular pop songs urging Sanchez to stay, with many waving flags or with their faces painted.
Some 12,500 supporters joined the rally, according to the Spanish government.
"I hope he continues, because Spain has to continue with him," Leonor Romero, 56, a councillor from Huelva, southern Spain, told Reuters.
"If not, it scares me.
"We are afraid of what could come."
Opposition parties have condemned Sanchez's move.
"I ask all citizens not to be fooled," Alberto Nuñez Feijoo, the leader of the opposition conservative People's Party, told a meeting in Tarragona in Catalonia.
"Spain does not have a problem - the one who has a judicial problem is Sánchez, his government, his party and his circle.
"Let them solve it."
Madrid's prosecuting authority said on Thursday it was appealing Wednesday's decision by a city court to look into the private complaint laid by an activist group linked to the far-right against Gomez over alleged influence peddling and business corruption.
Sanchez came to power in 2018.
