Police said 25,000 people gathered in central Madrid's Colon Square, where protesters unfurled flags and called on Sánchez to go, while demonstrations also took place in cities across Spain.
Vox leader Santiago Abascal denounced a "government of treason, insecurity and ruin" after recent changes to the criminal code and the approval of a new law against sexual violence.
READ MORE: Why Spain's right is vehemently opposed to changes to sedition law
He lambasted the planned abolition of the crime of sedition, of which nine separatist leaders were convicted over their role in the Catalonia region's abortive secession bid in 2017. An offence carrying a lower prison sentence will replace it.
"We have a government that governs against the people, lowers prison sentences for crimes, disarms the police," Abascal told his followers in the Spanish capital.
The right believes the modified criminal code, which should be in place by the end of the year, will encourage further attempts to separate the northeastern Catalonia region from Spain.
"We are being governed by separatists, people who don't want to be Spanish, that's why I'm here," said protester Cesar Peinado, a 65-year-old retired truck driver, accusing the government of "buying votes".
Abascal said sexual assaults had doubled since Socialist premier Sánchez took power in 2018 and denounced a law he claimed allowed rapists and paedophiles to leave prison earlier.
READ MORE: Why is Spain reducing prison sentences for rapists?
He was referring to a flagship government law against sexual violence that toughened penalties for rape but eased sentences for other sexual crimes, setting some convicts free after their jail terms were reduced.
María Dolores López, 58, told AFP she could "no longer put up with what this government is doing", citing its policy towards the Catalan separatists and its law against sexual violence.
"It isn't a coincidence that there's no security either," Abascal added, denouncing "a crazy minister who makes a law with the approval of the entire government, the political and media left so that rapists and paedophiles end up on the streets".
The ruling left-wing coalition has long drawn the ire of the right and far right for initiating a dialogue with Catalonia's pro-independence leaders, with large protests taking place in 2019 and 2021 over the talks.
Lacking a parliamentary majority, Sánchez's government has been forced since its formation to negotiate with Basque and Catalan separatists to pass bills.
The coalition says sedition is an antiquated offence that should be replaced with one better aligned to European norms.
The nine Catalan separatists initially sentenced to between nine and 13 years in prison under the sedition law were pardoned last year, also infuriating the right.
The failed independence bid sparked Spain's worst political crisis in decades, with then-Catalan leader Carles Puigdemont and several others fleeing abroad to escape prosecution.
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