Pakistan's premier even expressed that Nawaz did not say or imply that the Mumbai attackers were sent from Pakistan deliberately.
Abbasi said this while talking to senior journalists after an emergency meeting of the National Security Committee (NSC) - Pakistan's top civil-military body - that condemned Sharif's "fallacious" statement and termed it as "incorrect and misleading".
Sharif's response today on the controversy is contradictory to the stance taken by his party, the Pakistan Muslim League-Nawaz, whose president Shehbaz Sharif said on Saturday that the party "rejects all claims made in the report, be they direct or indirect", Dawn newspaper reported.
Referring to a 2016 meeting in which, according to Dawn, the civilian government had informed the military leadership of Pakistan's growing worldwide isolation, Nawaz said, "Even at that time, the same things? getting our house in order? were being discussed in the NSC meeting".
The video message was released as a response to Mr Sharif's allegations about the involvement of "non-state actors" in the Mumbai attack.
Prime Minister Shahid Khaqan Abbasi chaired on Monday a parliamentary meeting pertaining to the merger of Federally Administered Tribal Areas (Fata) with Khyber-Pakhtunkhwa.
Abbasi said he also held a meeting with Sharif after the NSC meeting and asserted that Sharif did not say what was reported in the media about the Mumbai attack.
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Mr Sharif said he will "speak the truth no matter what the consequences are".
Referring to the 2014 sit-in by the PTI and Tahirul Qadri, he said that he would reveal the names of the important characters behind it when the right time arrives.
"We should find out who laid the foundation of terrorism in the country", he asserted.
India blamed the Pakistan-based militant group Lashkar-e-Taiba (LeT) for the 2008 attack on the city of Mumbai.
Sharif's statement has left the Pakistan Army extremely anxious that "this will give more weight to India's narrative that Pakistan is not doing enough" with respect to the 26/11 trial, and could even put Pakistan on the blacklist of global financial trade agreements.
Mr Musharraf, who was the army chief during the Kargil War, also demanded that Mr Sharif should be tried for treason for his remarks on the 2008 Mumbai terror attack.