"The young men deserve the Federal Cross of Merit," Social Democrat defence expert Johannes Kahrs told Bild daily, referring to Germany's highest honour for civilians.
"What they've done is proof of their deep respect for their host country, Germany... It's hard to imagine greater integration (in the country). This is exemplary."
The top-selling daily Bild described the trio as "the Syrian heroes from Leipzig."
"Will they be fast-tracked to become German citizens?" it asked.
Several politicians also urged the government to swiftly grant the three asylum.
"What the three have done is a courageous and highly recognisable achievement," said the chairman of the parliamentary committee on interior affairs, Ansgar Heveling.
"Their asylum applications should be examined quickly... and surely there must be a way to reward them for their commitment," Heveling told Berliner Zeitung daily.
The three Syrians had unwittingly invited the 22-year-old fugitive Jaber Albakr to stay at their apartment in the eastern city of Leipzig.
They only realized later that Albakr was being sought by police, who on Saturday raided his apartment and found 1.5 kilos (over 3 pounds) of TATP, the homemade explosive used by jihadists in the Paris and Brussels attacks.
After seeing police's appeals for information in Arabic on Facebook, the Syrians quickly overpowered the fugitive, tied him up, and called in police officers to take him away.
Albakr had offered them money to allow him to go free, they later said.
"He tried to bribe us, but we told him he could give us as much money as he wanted, we wouldn't free him," one of the men told RTL television, speaking with his back to the camera and identified only as Mohamed A., for fear of reprisals.
"Then we got an electrical cord and tied him up until the police got there," he said.
"I was furious with him, I couldn't accept something like this - especially here in Germany, the country that opened its doors to us."
Their courageous action was not only celebrated by Germans, but also particularly feted on social media by tens of thousands of their compatriots who have sought asylum in Germany.
Neighbouring France had granted citizenship to an undocumented migrant from Mali, Lassana Bathily, after he saved shoppers' lives during a jihadist attack on a Jewish supermarket in Paris last year.
Three Americans who helped thwart a terror attack on a train in France last year were also awarded the Legion of Honour, the country's highest decoration.
Germany's domestic intelligence chief Hans-Georg Maassen said his service had received information that Albakr "initially wanted to target trains in Germany before finally deciding on one of Berlin's airports".
Investigators said explosives amassed in Albakr's apartment were "almost ready or even ready for use," and that he was apparently preparing a "bomb, possibly in the form of a suicide vest."