On Friday Puente said he was “not going to use any worker as a shield”.
But he said “many questions” arose as a result of the tragedy and he wanted to look at them “one by one”.
“If the investigation shows there is human error we will act in consequence of that,” he said.
The conservative People’s Party joined calls for Puente’s resignation after trade union CSIF called for the same earlier this week.
But Puente said on Friday he would not budge from his position.
“The easy thing for me would be to leave, but neither that fits with my character nor is it what the Prime Minister has asked me to do,” he said.
“I feel immense pain and immense sadness for the victims and their relatives… I cannot let this pain paralyse me though. We have to find solutions to this problem.”
The country is observing three days of mourning, as the families of victims and the survivors of the crash struggle to comprehend how it could have happened.
A 24-year-old athlete and a former government minister are among the victims of Wednesday’s disaster, but many families are still waiting for information from authorities about their loved ones.
Esther San Emeterio, whose 54-year-old brother Pepe is still missing, told reporters in Toledo, near Urda, that officials were forcing families to wait in “uncertainty”.
“We went to bed crying, outraged and full of shame,” she said. “We are desperate and I want all of Spain to know. How can they keep us like this?”
Additional reporting by Sergi Forcada Freixas
