Greste and producers Mohamed Fahmy and Baher Mohammed, who all work for the Al Jazeera TV network, were detained in December, accused of supporting a banned "terrorist organisation" - the Muslim Brotherhood - and trying to tarnish Egypt's image by broadcasting "misleading" news on the political situation.
Overnight, the three faced court for the first time since their arrest and were all denied bail. The case has been adjourned until March 6.
Egypt's ambassador in Canberra has been called to the Department of Foreign Affairs to hear of Canberra's displeasure, and Foreign Minister Julie Bishop has directly lobbied Egyptian officials.
But Professor Amin Saikal of the Centre for Arab and Islamic Studies at the Australian National University claims the Government should be mounting a far more assertive campaign.
"Publicly, the Abbott Government has remained somewhat muted on the issue," Professor Saikal said.
"Obviously they have called for the release of Peter Greste and all those sort of things, and our ambassador in parallel has been active on that front, but have they really unleashed an international campaign?
"What role did they play on the (UN) Security Council in relation to this issue? How much have they tried to mobilise Western public opinion in support of the release of Peter Greste?
"To what extent have they really forged consensus among Australia's allies to put pressure on the Egyptian government?"
It has been a turbulent three years for Egyptian politics and Al Jazeera.
In January and February of 2011, millions took to the streets in the Arab Spring, ultimately ending Hosni Mubarak's 31-year reign.
Al Jazeera covered it all and was hailed as the voice of democracy.
The Muslim Brotherhood - the region's oldest Islamist political group - won power in democratic elections in 2012, and Al Jazeera played a pivotal role in covering the historic ballot.
Over the decades, the US had grown comfortable in dealing with Mubarak's military rule and there was concern in Washington over the rise of the Islamists.
In July 2013, political and economic mismanagement led to widespread disillusionment, a coup deposed Islamist president Mohammed Morsi, and an interim military government was formed.
The Muslim Brotherhood was outlawed, and Egypt's new military rulers claimed Al Jazeera was a mouthpiece for a terrorist organisation.
Abbott Government 'not really in favour of the Islamists to assume power'
Professor Saikal believes Canberra prefers dealing with the current leadership in Cairo and this has influenced the official response to the Al Jazeera arrests.
"The Abbott Government is not really in favour of the Islamists to assume power in the region," he said.
"Therefore, in ideological terms, it has to be on the side of this military-backed government in Egypt."
Professor Saikal says Greste and his colleagues have been caught up in a regional power play involving Egypt, Qatar and Saudi Arabia.
"Egyptian authorities want to send a very clear signal to all those reporters and networks that they don't want contact with the Muslim Brotherhood or any opposition group, and secondly to send a signal to Doha to stop interfering and stop being so critical of the overthrow of the Morsi government," he said.
The Doha-based Al Jazeera network is owned by the government of Qatar.
Professor Saikal says it is highly significant that Qatar was the only nation to provide substantial funding to the Muslim Brotherhood government of Mr Morsi.
"I think Al Jazeera is a creation of Qatar. It is highly critical of what is going on in other Arab countries and it has touched a number of subjects which have been taboo in the past, and yet Al Jazeera has been reporting nightly on those issues," he said.
Professor Saikal says Saudi Arabia has been incensed by the broadcasts of the most-watched channel in the Arabic-speaking world, and by an "upstart" Qatari government the Saudis fear is attempting to challenge their regional dominance.
"Qatar has tried to emerge as an influential player in the region by not only hosting the largest American military base - in Qatar - but making use of its oil riches by buying more friends in the region," he said.
"[That] had been partly designed to counter the attitude of the Saudis [as] the Big Brother and also counter any historical ambitions that the Saudis may have over (controlling) Qatar.
"As soon as the Muslim Brotherhood was toppled by the military in Egypt, Saudi Arabia moved very quickly not only to support the coup and the formation of a military-backed government in Egypt, but also to provide immediate financial assistance.
"The Saudis immediately promised $US4 billion but also got its other allies - Kuwait in particular - to make equal contributions, basically amounting to $US12 billion assistance to the military-backed regime in Egypt which helped to bail it out of serious financial and economic difficulties.
"After the coup in Egypt, the Saudis tried to clip the wings of the Qataris - cut the Qataris down to size. And Al Jazeera really to some extent has been caught in this cobweb of difficult relationships between Qatar, Egypt and Saudi Arabia."
None of this will be of comfort to Greste, Fahmy and Mohammed, who have been languishing in jail since their arrest on December 29.
The trio's lawyer, Farag Fathy, says another 17 people have been indicted in the case.
Seven are linked to Al Jazeera, but Mr Fathy says the other 10 are alleged members of the Muslim Brotherhood who are accused of making anti-government propaganda videos, and should be separated from his defendants.
Australian journalists sign petition calling for Greste's release
The Australian journalists' union, the Media, Entertainment and Arts Alliance (MEAA), has lobbied on behalf of Greste, organising a petition calling for his release, which was signed by more than 1,000 journalists and then delivered to the Egyptian Embassy in Canberra.
MEAA federal secretary Chris Warren says it is important to distinguish that Greste and his two colleagues were working for Al Jazeera's highly regarded English-language channel, not the separate Arabic-language service.
"There is a view that Al Jazeera Arabic was supportive of the Morsi government because of the relationship between the Qatari government and the Morsi government," he said.
The Egyptian authorities really need to let them go, let them get on with their job and accept that that's the price of reporting in the modern age.
MEAA federal secretary Chris Warren
"A lot of that criticism has occurred more with the Al Jazeera Arabic service than with the Al Jazeera English service, and it is clear that the view of the Egyptian government is that they see Al Jazeera as little more than an arm of the Qatari government and the Muslim Brotherhood and effectively that's what they've been arrested and charged with.
"In a sense that's immaterial anyway as media organisations have a right to report from a particular standpoint, and it's possible to do that while still acting in an independent and ethical way, which from all the evidence is what Peter and his team seemed to be doing.
"The Egyptian authorities really need to let them go, let them get on with their job and accept that that's the price of reporting in the modern age."
Mr Warren says while Ms Bishop has played "a very constructive role" in making representations to Egyptian authorities, the MEAA also requested the Prime Minister become involved.
"We joined the family in asking Tony Abbott to directly intervene," he said.
He says he has not heard back from the Prime Minister's office.
"My view is that ... the Foreign Minister is doing what can be done," Mr Warren said.
"I suspect that there's a reluctance to have the Prime Minister to make a request when it is likely to be rejected and what that could do to the ongoing relationship."
Washington appears less concerned by such sensitivities.
Greste's cause has been championed by US president Barack Obama, with the White House urging the Egyptian government to drop all charges.
"The restrictions on freedom of expression in Egypt are a concern - and that includes the targeting of Egyptian and foreign journalists and academics simply for expressing their views" Mr Obama said earlier this month.
Disclosure: Mark Corcoran worked as a reporter/producer for ABC TV's Foreign Correspondent for 15 years. Several of his reports were re-broadcast on both Al Jazeera English and Al Jazeera Arabic.