Socialist leader Sanchez, who took over as prime minister earlier this month after conservative Mariano Rajoy lost a vote of confidence, criticised De Gea two years ago amid sexual assault claims against the Manchester United player.
Last week, when Sanchez came to see the Spanish team off ahead of the World Cup in Russia, De Gea was pictured with his hands in his pockets, remaining on the fringes of the group as teammates applauded the premier's arrival.
"I accepted his apologies politely," Spanish media quoted the goalkeeper as saying.
"The thing is, though, that what he said at the time was in public so I think his apologies should also be made publicly."
Sanchez made his comment after a woman accused De Gea of organising a party where women were obliged to have sex with footballers.
De Gea denied the accusations, which an investigation found to be false.
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