Greste was not named on the list of about 100 pardoned prisoners - which included colleagues Mohamed Fahmy and Baher Mohamed - after being convicted in absentia last month for collaborating with a terrorist organisation.
Fahmy and Mohamed were released from prison within hours of their pardon being announced.
"(A pardon) would mean all the difference in the world. I still have, as far as I know, a conviction hanging over my head and a criminal record as a convicted terrorist," Greste told ABC radio on Thursday.
"If we're going to undo that injustice, if we're going to do this right, then he (President al-SiSi) needs to follow through so that everyone who was convicted in this case... has their convictions quashed.
The state-run MENA news agency said a third person from the case - which included multiple other defendants along with Australian journalist Peter Greste - was also pardoned, but was not identified by name.
Greste was deported earlier this year.
A tweet from Fahmy's account on Wednesday afternoon said: "Thank you to all the supporters sending us the news, we have heard and are very happy. AJ Staff is Free!"
"I don't know what to say. It is done. Thank God, thank God," Fahmy's brother, Adel, said when reached by The Associated Press by phone from Kuwait.
The three were sentenced to three years in prison last month for airing what a court described as "false news" and biased coverage. There was no immediate comment from the Al Jazeera network, which is based in Qatar.
Prominent Egyptian activists Yara Sallam and Sanaa Seif were among about 100 people pardoned by President Abdel-Fattah el-Sissi, according to state media MENA, on the eve of the major Muslim holiday of Eid al-Adha, when Egyptian presidents usually pardon convicts for health or other reasons.
The pardon also comes a day before el-Sissi is to travel to New York to attend the United Nations General Assembly.
Fahmy's lawyer, Khaled Abu Bakr, confirmed the pardon him and said he hopes it will be "repeated with many others jailed".
"I was sure the president was going to issue such a decision. Mohammed is a professional and innocent journalist," Abu Bakr told AP.
"This decision will have positive impact on the media and international level."
On Tuesday, Greste attended the dedication of a war correspondents memorial at the Australian War Memorial in Canberra, where Prime Minister Malcolm Turnbull spoke to him and vowed to press Egypt for a pardon for him and his colleagues.
WATCH: Peter Greste gets news from Egypt of his colleagues' release on the set of The Chaser's Media Circus
