Thousands of people have protested in cities across Spain over the government’s handling of the influx of migrants to the Spanish exclave of Ceuta on the north African coast.

Spanish opposition parties accuse Prime Minister Pedro Sánchez of abandoning the residents of Ceuta, while the government says right-wing parties are exploiting the crisis.

On Wednesday a police report said Moroccan security forces showed “total permissiveness” during the unprecedented influx, days after Sánchez insisted Morocco was not responsible.

He has blamed trafficking gangs and online misinformation for encouraging people to cross the border. Morocco has denied orchestrating or being involved in the mass crossing.

At least 72,000 migrants crossed from Morocco into Ceuta on 30 and 31 July and although most have returned, as many as 5,000 remain in makeshift camps or scattered across the city’s streets or on the beach – leading to unrest in the autonomous city in North Africa and a crisis for Sánchez.

There have been near-daily protests by locals, with demonstrators calling for the migrants to be sent back to their countries of origin or redistributed across Spain.

Wednesday’s rallies were called by city councils across Spain where opposition parties – the conservative Partido Popular (PP) and the far-right Vox party – govern or have significant popularity.

Demonstrators called on Sánchez to resign.

PP leader Alberto Núñez Feijóo was at the rally in Madrid, where more than 50,000 people gathered, according to government figures.

“A Spanish city has been invaded, occupied and, unfortunately, this happened with the knowledge of the Government of Spain,” he said.

Vox leader Santiago Abascal meanwhile said Sánchez was “at the service, like a lackey, of the Moroccan regime”.

There was also a major rally in Ceuta itself, with participants chanting: “Ceuta is not for sale, Ceuta must be defended.”

“The response has been inadequate, late and, to top it all, has involved a complete dereliction of duty on the part of the government,” 45-year-old teacher David Hernandez told Reuters.

“We cannot be second-class citizens, and our border must not be sidelined.”

Pressure on Sánchez’s government has intensified after Spanish media said the report submitted by the National Police’s National Immigration and Borders Centre (CENIF) to the National Court pointed to the involvement of Moroccan gendarmes in the migrant crossings.

The police report claimed that the Moroccan police deployment around the border “was clearly smaller than usual” and cited migrants who spoke of a “passive attitude” as the crossings happened.

However the report did not categorically accuse Morocco of being behind the influx.

Morocco has a long-standing claim over Ceuta and its fellow autonomous city of Melilla, which have long been a flashpoint in diplomatic relations between the two countries.

A large number of social media posts appeared in August portraying the border fence between Morocco and Ceuta as safe and easy, even though at least 100 people died while trying to swim around the border fence, according to figures from the mayor.

Spanish fact-checking website Maldita said before 30 July, when the influx began, messages circulated on Moroccan social media encouraging people to attempt the crossing, after a June ruling by Spain’s Supreme Court.