According to the member of the party, Michael Kretschmer, German intelligence does not have the right to access "the core profile" of asylum seekers.
"This should be changed. We want the German intelligence services to have access to this file as well," Kretschmer said, cited by German newspaper Die Welt.
Earlier, a Syrian man was captured in the eastern German city of Leipzig after two days on the run, local police said early Monday. The arrest of the 22-year old Jaber al-Bakr came a few days after the police discovered explosives in his Chemnitz apartment south of Leipzig.
Merkel has been repeatedly criticized for her open-door policy toward refugees, which resulted in millions of undocumented migrants from war-torn regions entering the country.
According to German Minister of the Interior, Thomas de Maizière, parallels can be drawn between the incident in Leipzig and the deadly attacks in France and Belgium.
"The preparations in Chemnitz resemble the preparations for the attacks in Paris and Brussels," de Maizière said.
France has been hit by deadly terror attacks since 2015. The deadliest of these attacks took place in Paris in November last year and resulted in 130 people killed.
On March 22, a series of blasts hit Brussels Airport and a metro station located near the EU institutions in the center of the city, killing 32 and injuring over 300 people. Daesh, outlawed in many countries including Russia, claimed responsibility for the attacks.
