If Meimarakis fails within the three-day limit, the next in line to try would be the head of the Nazi-inspired Golden Dawn party, and potentially the centrist To Potami, which each have the same number of seats in the 300-member Parliament.
None are believed to have enough allies to gain Parliament's support.
However, hardliners in Tsipras' radical left Syriza party said yesterday they intended to split from the party and form their own separate group in Parliament.
If that breakaway group numbers more than the 17 seats held by Golden Dawn and To Potami, it would become the third-largest behind Syriza and New Democracy, and would be able to receive the mandate from the President to form a Government.
If no party can form a coalition to govern, Parliament will be dissolved and elections held within the next month.
Announcing his resignation in a televised address yesterday, Tsipras said he secured the best deal possible when he agreed to a three-year, 86 billion ($146 billion) bailout from other eurozone countries to save Greece from a disastrous exit from the shared euro currency.
But the deal came with strict terms for more belt-tightening.
Tsipras' reversal in accepting the demands by creditors led to outrage among hardliners in his Syriza party. About one in four Syriza lawmakers refused to back the bailout's ratification in Parliament last week, which was approved only with backing from Opposition parties.
Greece's European creditors did not appear dismayed by Tsipras' move. But Moody's credit rating agency warned the snap election "potentially puts future [rescue loan] disbursements at risk".
The political uncertainty took its toll on Greece's stock market, the Athens Stock Exchange closing 3.5 per cent down.
Tsipras had delayed a decision on whether to call new elections until after Greece received its first instalment from the new bailout and made a debt repayment to the European Central Bank; it did both.
"Now that this difficult cycle has ended ... I feel the deep moral and political obligation to set before your judgment everything I have done, both right and wrong, the achievements and the omissions," he said.
Tsipras insists he had to accept the unpalatable bailout terms to keep Greece in the euro. He is betting on a stronger mandate if polls are held before voters feel the impact of the new steep tax hikes and spending cuts.
He acknowledged the bailout deal was not what his Government had wanted.
"I wish to be fully frank with you. We did not achieve the agreement that we were hoping for before the January elections," he said. "But [the agreement] was the best anyone could have achieved.
"We are obliged to observe this agreement, but at the same time we will do our utmost to minimise its negative consequences."
Quoting Turkish left-wing poet Nazim Hikmet, he added "Our best days have yet to be lived".
Greek banking is still restricted under capital controls imposed in late June to stem a bank run.
There are weekly limits on cash withdrawals and Greeks can only transfer up to 500 abroad per month. Companies have faced problems paying suppliers outside the country, with all international payments requiring a laborious process of approval.
Some analysts took the early election news as an indication Greece would struggle to implement the terms of its latest bailout.
Teneo intelligence analyst Wolfango Piccoli said while Tsipras' gamble could pay off politically, it probably would delay the first review of the new bailout programme because "the caretaker Government will not be able to implement any meaningful policy measures".
Rocky road
Total debt pile: €320b ($543.8b)
New bailout package: €86b
Debt to be settled: By 2057
How did Greece get here?
In January, the leftist Government of Syriza promised to end years of austerity measures but remain a member of the eurozone.
What went wrong?
Negotiations descended into acrimony. Creditors threatened the country with an exit, forcing Prime Minister Alexis Tsipras into submitting to harsh bail-out conditions.
What now?
Greece is still in the euro but needs another €86 billion over three years to stop going bankrupt. Negotiations over this new deal have hit some buffers as the IMF is reluctant to stay involved.
- Telegraph Group Ltd, AP
