Amid media reports that Di Maria would miss the remainder of the tournament, Martinez said doctors would assess "day by day" the winger's evolution to see whether he can play Argentina's last game in the tournament, be it the final or the match for third place.
Martinez told reporters at the Cidade do Galo training complex in the outskirts of Belo Horizonte that Di Maria's "is one of the least serious among muscular injuries."
The Real Madrid winger felt a pang 28 minutes into Saturday's quarter-final against Belgium, following a run and a shot. He tried to keep going, but he left the pitch in pain four minutes later.
Argentina doctors carried out preliminary tests at the Estadio Nacional in Brasilia, and a more thorough evaluation upon arrival in Belo Horizonte. The tests were repeated Sunday, to see Di Maria's evolution after one day.
"We have everything at our disposal for Angel to be able to recover. He will of course not be playing Argentina's next game, and after that game we will assess his condition day by day to give him the chance to play the last match," said Martinez.
Di Maria has been a crucial player in Argentina's World Cup campaign, which has led them to a semi-final they had not played since Italy 1990.
Martinez also said Sunday that striker Sergio Aguero has fully recovered from a muscular injury in his left thigh and is "ready to play" after three football training sessions without trouble.