The accused, Habte A., is a 40-year-old Eritrean wanted in Switzerland for domestic violence.
On July 25, the man fled his home after assaulting his wife in the presence of his children, who were one, three and four years old. He locked them up with a neighbour, whom he allegedly tried to strangle.
"I will direct the situation to establish intelligent controls at the border," German Interior Minister Horst Seehofer told the "Der Spiegel" digital journal.
It is estimated that in 2018 about 43,000 people entered the country irregularly.
Seehofer will present a new plan for selective border control in September, according to "Der Spiegel", although he hasn't discussed it yet with Chancellor Angela Merkel, said the report cited by Efe news.
The day after the boy's death at Frankfurt station, Seehofer announced his intention to both strengthen surveillance in train stations and installing security fences, similar to those that have been installed in some European cities.
Habte A. also threw the murdered boy's 40-year-old mother onto the railway, but she managed to reach safety.
He targetted another 78-year-old woman who was also on the railway platform.
The case has sparked a debate in Germany about safety at train stations, while the extreme right has used the murder to attack the Muslim community.
The motive of the murder is not yet known, although authorities said that the alleged murderer had been in psychiatric treatment for a few months. For now, they have ruled out any terrorist link and radicalization.
( With inputs from IANS )