A Moroccan security source said migrants from sub-Saharan Africa had drowned when three vessels sank off Al Hoceima coast on that day.
The survivors said they were taken to the border with Algeria, and that the Moroccan authorities have tried to cover up the incident.
About 70 migrants left Morocco on the morning of April 28 in an attempt to reach Spain, the newspaper said. Two hours later, they came across a Moroccan naval vessel and soldiers approached the migrants in a motor launch.
"One of the soldiers jabbed a knife into the rubber and told us 'now go to Spain if you want,'" one of the survivors, identified as Campos, said in Oujda, an eastern Moroccan border town.
"We tried to patch it up and we continued on with difficulty, but I think that we would have made it if they had not returned," said another survivor, Erick O, a Nigerian fisherman, who said his wife and three-year-old daughter were among those who had drowned.
The Moroccan launch returned and a soldier began threatening the migrants with a knife.
"We asked them to take us back with them to Morocco because, with the boat in the state it was, it was almost impossible to continue," Campos said.
"We begged them to look at our children and babies."
A Moroccan officer then took the knife and "punctured the boat four times in different places," following which it sank in a few seconds.
Another Moroccan launch came to help the drowning migrants, El Pais reported.
A Spanish human rights group has said more than 900 potential migrants died at sea trying to reach Spain in 2007, the majority at the start of their journey close to the coast of north Africa.