The mass crossing into Ceuta, a Spanish-held spit jutting into the Mediterranean from Morocco, caused division in Europe, with Italy threatening to suspend the EU's internal open border scheme.
At the gates into Ceuta, Moroccan authorities had deployed water cannon trucks and pushed people back.
The charred remains of a bus and seven cars could be seen nearby from clashes with the crowds.
Spanish authorities said they would try to expel those who had entered illegally as quickly as possible, despite a court ruling that has put some new restrictions on special "border rejection" rules that allow immediate expulsions.
Prime Minister Pedro Sanchez was due to visit Ceuta on Friday with Interior Minister Fernando Grande-Marlaska.
Ceuta and Melilla, another Spanish autonomous city in northern Morocco, have the European Union's only land borders with Africa.
The two cities are each home to around 85,000 people.
Both cities periodically experience surges in attempted crossings by migrants seeking to reach Europe, but nearly 50,000 crossing in a single day appears to be unprecedented.
Spain described it as the biggest crisis since at least 2021.
Territorial Policy Minister Angel Victor Torres said on Friday that among factors contributing to the surge might have been a ruling by Spain's Supreme Court in July that migrants intercepted at sea while attempting to reach Ceuta or Melilla cannot be summarily returned under special rules.
Torres told a local radio station the Spanish government had reacted immediately to the surge and would proceed to eventually return the migrants, while respecting court rulings and migrants' rights.
On the Moroccan side of the border, thousands of migrants streamed into the town of Fnideq overnight despite a reinforced deployment of security that foiled most attempts to cross.
Although the crossing appeared blocked, groups moved along the coast seeking routes around the fence. Some prepared to swim.
In a post on X, Spain's Guardia Civil police association AUGC said there had been too few police in place to monitor the fence during the surge on Thursday, making them unable to stop it.
"Migratory policies require a deep revision that addresses the reality of the south border and guarantees the respect of the dignity and human rights of the migrants and refugees who arrive to Ceuta," said a joint statement by several local migrant groups, saying resources in Ceuta were insufficient.
Migration is a sensitive issue across Europe, where right-wing parties have surged in the decade since a 2015 crisis when more than a million people crossed the continent mainly on foot and sought asylum, most fleeing war in Syria.
Italy's right-wing prime minister, Giorgia Meloni, said her country was prepared "to intervene with extraordinary measures to defend the borders and the safety of citizens, including the suspension of the Schengen Area with Spain", referring to the EU's internal border-free zone.
While Spain's Socialist government says it remains firm over illegal crossings, it says immigrants help strengthen the economy and has offered a mass amnesty that saw hundreds of thousands of people seek citizenship in the past year.
"The images coming from Ceuta show how the Madrid government's decision to grant Spanish, and therefore European, citizenship to over 500,000 irregular immigrants is profoundly wrong and encourages human trafficking," Italy's Foreign Minister Antonio Tajani wrote.
Spanish Foreign Minister Jose Manuel Albares replied that Tajani's message was "inappropriate", and said Spain expected "solidarity and not partisan demagoguery" from its partner.
He said he would summon the Italian ambassador to protest.
