The death toll, which could still rise, is by far the worst recorded in years of attempts by migrants to cross into Melilla, one of Spain's North Africa enclaves which have the EU's only land borders on the continent.
Images on Spanish media on Friday showed exhausted migrants lying on the pavement in Melilla, some with bloodied hands and torn clothes.
By Saturday, calm had returned to the border area, with Moroccan security forces lightly deployed and no migrants to be seen.
Mohamed Amine Abidar of the AMDH said migrants, who are often rounded up by authorities and taken to cities further south, had "probably moved away for fear of being displaced".
The AMDH demanded a "comprehensive, quick and serious enquiry, while the Democratic Labour Organisation (ODT) trade union urged the Moroccan government "to investigate this tragedy and do what is needed" both for migrants and police.
In Spain, Sanchez's left-wing coalition partner Podemos also called for a probe.
The mayor of Melilla, Eduardo de Castro, said the stampede had been "violent" but called the Moroccan response "disproportionate".
