The high court had commuted Baig's death sentence to life imprisonment in 2016.
Baig has also moved the apex court against his conviction and sentencing by the trial court and the high court.
A bench of Justices D Y Chandrachud and M R Shah admitted the cross appeals and said it will hear them.
On July 22, 2016, the apex court had sought Baig's response on the Maharashtra government's appeal.
The government's plea challenged the March 17, 2016 judgement of the Bombay High Court which also acquitted Baig of serious charges under various sections of the Unlawful Prevention (Activities) Act and the Indian Penal Code (IPC), including sections 302 (murder) read with 120-B (criminal conspiracy).
The high court had convicted 32-year-old Baig for offences under the IPC's section 474 (possessing a document knowing it to be forged with intent to use it as genuine) and under section 5(b) of the Explosive Substances Act, relating to punishment for making or possessing explosives under suspicious circumstance.
Baig, who was alleged to be a member of banned terror outfit Indian Mujahideen, was arrested in September 2010 from Latur in Maharashtra for his involvement in the blast at German Bakery, a popular eatery in Pune's Koregaon Park area. The blast killed 17 people and injured 58, including some foreigners.
In 2013, he was convicted and awarded death sentence by the trial court.
The state government's plea had claimed that the high court had not relied upon the evidence which showed that Baig had travelled from Latur to Mumbai and stayed at a lodge for the purpose of entering into a conspiracy or "for giving final shape to terrorist act or in furtherance of his terrorist activities".
"Prosecution witness 93 was the autorickshaw driver who saw the respondent (Baig) with the planter of the bomb which proves the last seen theory. In the test identification parade, the autorickshaw driver identified the respondent.
"In spite of that, the high court held that the plea of the prosecution that the respondent was last seen with planter of the bomb does not get credence," the plea said.
The further said, "The high court does not consider that there was a definite connection between the explosive recovered from the possession of the respondent and the explosive used in the bomb."
Besides Baig, Qateel Siddiqui was also arrested in the case. He died in Pune's Yerawada jail in a scuffle with other inmates.
The other wanted accused are Indian Mujahideen operatives -- Mohsin Choudhary, Riyaz Bhatkal, Iqbal Ismail Bhatkal, Fayyaz Kagzi and Sayyad Zabiuddin Ansari.
Yasin Bhatkal, who had allegedly planted the bomb in the eatery, was arrested in August 2013. The case against him is pending before the trial court.