Thousands of migrants remain in Ceuta after a mass rush from Morocco last week, the enclave's president has said.

At least 72 migrants died, including some who drowned and others who were killed in a stampede to cross a breakwater barrier, Spanish authorities said on Sunday, while Morocco reported 11 deaths on its side of the border.

Spain estimates that around 69,500 of the migrants have returned to Morocco over the past four days, exceeding initial estimates of about 50,000 arrivals in Ceuta on Thursday.

Many of them fled due to shop closures, receiving a hostile response from locals and being unable to travel on to the Spanish mainland.

Between 3,000 and 5,000 migrants remained in the enclave, Ceuta's president Juan Jesus Vivas told broadcaster Telecinco, adding that its two migrant reception centres - one for adults ​and another for minors - had "collapsed".

The city was processing 862 migrant minors, who enjoy special legal protections from deportation, local official Alberto Gaitan said.

Hundreds of migrants set up camp on a beach in Ceuta on Monday as local authorities struggled to cope with the thousands who had stayed in the tiny territory.

Video showed scores of migrants, most of them from sub-Saharan Africa, ⁠lying on El Trampolin beach. Many were wrapped in towels to shelter from the wind, while army and police vehicles patrolled the road behind ​them.

Meanwhile, Spanish authorities were continuing to search for bodies in the waters that tens of thousands of migrants had breached days earlier.

The migration crisis in Ceuta is being investigated by Spain's top court - the Audiencia Nacional - Sky News understands.

The high court's Judge Maria Tardon has ordered the Spanish National Police's Central Unit for Illegal Immigration (UCRIF) to file a report with the Spanish Public Prosecutor on "the massive irregular entry of citizens from Moroccan territory that has taken place in Ceuta in recent days, especially on July 30 and 31".

This will allow it to clarify "whether the event was a concerted action directed by any criminal organisation or group, and to gather any identifying information on those who may have participated in such actions, if there is any evidence of this".

The judge has opened preliminary proceedings for possible crimes against the security and independence of the Spanish state.

The crisis has sparked anti-immigration rhetoric across Europe and diplomatic tensions within the European Union over border policy, with Spain accusing some partners of an unhelpful and polarising response.

On Friday, Italy temporarily suspended its open-border Shengen agreement with Spain, re-imposing border controls for air and sea.

Foreign minister Jose Manuel Albares said on Monday that Spain had ​previously supported other EU countries during migration crises and now expected them to respond in turn.

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The bloc has called an emergency video conference meeting of interior ministers on Tuesday to discuss the crisis.

Morocco's Interior Ministry on Sunday said the rush of migrants was caused by social media misinformation, human trafficking networks and misinterpretation of a Spanish court ruling banning immediate ​returns of migrants intercepted at sea.

Spanish intelligence services have concluded that Morocco did not plan the mass crossing, but allowed it to happen, according to reports by El Pais and Cadena SER radio, citing officials familiar with the matter.

Moroccan border controls were gradually eased during July and were allegedly removed as migrants surged towards the Tarajal crossing during Morocco's Throne Day holiday, the ​reports said.