The 14, including one woman, drowned on Thursday while trying to reach the Spanish territory of Ceuta from a beach in neighbouring Morocco. Other migrants tried to storm through a land checkpoint.
Spanish media cited migrants alleging that police fired into the sea where the Africans were swimming, as Moroccan and Spanish security forces tried to repel them from Ceuta.
Spanish authorities said police in Ceuta used rubber bullets to ward off the migrants but that they fired them in the air and did not target anyone directly.
"We did not use anti-riot equipment when the immigrants were in the water," said the head of the Spanish government's delegation in Ceuta, Francisco Antonio Gonzalez, speaking on the radio on Friday.
Spain's opposition Socialist Party called on Interior Minister Jorge Fernandez Diaz to appear in parliament to answer questions on the deaths of the nine migrants.
In Morocco the head of the Northern Human Rights Observatory, Mohamed Benaissa, told AFP on Thursday that several migrants were hurt as Spanish police tried to repel them. He said most of the migrants were from Cameroon.
The Spanish government delegation said late Thursday that "rubber bullets were fired in the air, over a six-metre fence, never against people", by Spanish police to ward off the migrants trying to cross by land.
Morocco, under pressure from Spain, is trying to stem a stream of sub-Saharan African migrants, who head to its northern shores in a desperate quest to reach mainland Europe.
Ceuta and Spain's other north African enclave, Melilla, have the European Union's only land borders with Africa.
Hundreds of migrants headed out from the Moroccan town of Fnideq in a mass attempt to cross or circumvent the six-metre (20-foot) fences that mark the land border with Ceuta on Thursday, officials on both sides said.
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Gonzalez said the migrants were "very violent" and threw rocks at the Moroccan and Spanish security forces.
A spokeswoman in Spain for the United Nations refugee watchdog UNHCR, Maria Jesus Vega, expressed "dismay and great sadness" at the deaths.
"It worries us that people who need international protection and are risking their lives to get to safe countries, are losing their lives trying to enter the countries of the European Union."