Officials said 70 people injured in the train accident remained hospitalized on Sunday, 22 in critical condition.
Mr. Iglesias was among survivors and witnesses who began to give evidence to police on Sunday.
Meanwhile, authorities said forensic experts have identified the last three bodies among the 79 dead.
Victims have been reported from France, Algeria, Brazil, the Dominican Republic, France, Italy, Mexico and the United States, but officials have not publicly identified each victim or his or her nationality.
Mourning continued throughout Spain, with Sunday church services being held in remembrance of the dead. A large funeral Mass is planned for Monday afternoon in Santiago de Compostela, and the prime minister and royal family are expected to attend.
The crash has cast a pall over the town, a Catholic pilgrimage site. Santiago officials were preparing for the religious feast of St. James of Compostela, Spain’s patron saint, but canceled it after the crash and turned a local sporting arena into a morgue.
• Harold Heckle contributed to this article from Madrid.