Christian Democratic Union (CDU) MP and security policy expert Wolfgang Bosbach told Welt newspaper that the government wants to fix a legal loophole.
Although the law currently permits the authorities to withdraw a person's passport on suspicion that they may leave the country to join a terrorist group, there is no such provision for identity cards.
German citizens are able to travel to the war zone stretching across Syria and Iraq via Turkey using only their national identity card to pass through border checks, rather than a passport.
By visibly marking the ID cards, the government wants to help border officials spot those who may be travelling to join jihadist groups.
Social Democratic Party (SPD) deputy leader in the Bundestag Eva Högl agreed with her coalition colleague, telling Welt that the party wants to at least examine the plans.
“The number of people taking this route [through Turkey] is rising steeply,” CDU deputy leader in the Bundestag Andreas Schockenhoff told the Passauer Neue Presse.
Schockenhoff said that he was in favour of even stricter changes to the law, such as ending the validity of the identity card for travel outside the country.
Fighting terrorism on two fronts
Germany is making moves against Iraq- and Syria-based terrorism both at home and on the front lines.
Seven of its soldiers arrived in Iraq five days late on Thursday night to instruct Kurdish troops fighting the Islamic State (Isis) in the use of weapons being delivered from the German army (Bundeswehr).
They left Germany last Friday, hoping to be in Irbil, north Iraq by Saturday, ahead of an equipment delivery, but were held up by a series of delays.
The training team, including six paratroopers and one medic, were initially delayed when there was a problem with their plane before take-off in Schleswig-Holstein.
They planned to make a short stopover in Bulgaria but were delayed there for five days when their plane was again hit with a defect.
They had to wait for a replacement machine and also for clearance from Iraqi authorities to arrive in the country.
The first plane taking German arms to the Kurds left in the early hours of Thursday following a 12-hour delay. It carried 27 tonnes of weapons and ammunition, including 50 anti-tank rocket launchers, 520 rifles and 20 machine guns.
Hours before the flight landed, defence minister Ursula von der Leyen made a surprise visit to Irbil to meet Kurdish leaders and visit a German training camp. “I want to assure you that we stand with you in this task,” she said.
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