Opinion polls suggest the PP, Citizens Party and Vox would win a majority of seats in parliament if early elections were held.
An estimated 45,000 people packed into the capital's Plaza de Colon, many of them waving Spanish flags and signs reading "Stop Sanchez" and "For a united Spain, elections now!"
They are opposed to Prime Minister Pedro Sanchez's proposal to hold talks with Catalan pro-independence parties.
Speaking at a Socialist party event in northern Spain, Sanchez reminded his political opponents that when he was an opposition leader, he stood by Rajoy on the situation in Catalonia even after separatist regional officials staged an October 2017 independence referendum in defiance of Spanish courts. Some banners at the rally read "Sanchez, liar" and "Spain is not negotiable and can not be sold".More news: Emergency as polar bears invade Russian town
Sanchez came to power in June with the support of Catalan nationalist parties, which voted with him in a no confidence motion against former Prime Minister Mariano Rajoy, whose PP was embroiled in a corruption scandal.
The government is squeezed on both sides of the Catalan issue: Deputy Prime Minister Carmen Calvo said on Friday talks were on track to fail because Catalan pro-independence groups had rejected the government's proposed framework.
Mr Sanchez is trying to cobble together support to pass a national budget and will need votes from the Catalan separatists to pass it.
The rally was called by the opposition center-right and far-right parties, which claim Madrid is betraying the Spanish people by caving to pressure from Catalan separatists. The Catalan groups want a referendum on independence included on the agenda, which Madrid will not accept.More news: ‘The Lego Movie 2' opens No. 1 but everything is not awesome
"The government is giving many things to supporters of Catalan independence and is going to break Spain apart", said Raquel García, 76, who was carrying a Spanish flag.
"The unity of Spain means uniting Spaniards and not confronting them as the right wing is doing in Plaza de Colon today", he said.
Despite the government's concession, Catalan separatist parties still refuse to back the government's 2019 budget.
The political tensions come as a highly-sensitive trial at Spain's Supreme Court starts on Tuesday for 12 leaders of the Catalan separatists, who face charges including rebellion for their roles in a failed secession attempt in 2017.More news: No. 9 Michigan State trounces Minnesota