The leaders of the Popular Party, Alberto Núñez Feijóo, and of Vox, Santiago Abascal joined the protest by hundreds of thousands of people in the centre of Madrid, bringing the capital to a standstill.
Sánchez's Socialist party finished second in an inconclusive July general election but he reached deals with several smaller parties to back him in the parliamentary vote for another term, including Catalan and Basque separatists.
To win the support of two Catalan separatist parties, he agreed to grant an unpopular amnesty to hundreds of people facing legal action for their role in Catalonia's separatist movement over the past decade.
That includes the wealthy northeastern region's failed secession bid in 2017 that involved a violence-marred referendum that was banned by the courts and followed by a short-lived declaration of independence.
The agreements with the Catalan parties also included opening talks on the possibility of holding an authorised referendum for independence for the region but within the legal framework of Spain's Constitution.
Sánchez has repeatedly said that he would not permit a vote that could break up Spain.
Critics say the amnesty is a self-serving measure to allow Sanchez to remain in power and accuse him of trampling on the rule of law.
For more than a week, thousands have congregated each night outside the Socialist party's headquarters in Madrid in rallies organised by the far right against the amnesty. Some protests have turned violent.
"We will continue to support all mobilisations and all calls to oppose" this "government born from an unconstitutional pact," said Vox leader Santiago Abascal, who has called the amnesty deal a "coup d'etat".
In a sign of the tensions the amnesty has sparked, dozens of retired right-wing generals issued a manifesto on Friday calling on "those responsible for defending the constitutional order" to "remove the prime minister" and "call" new elections.