Israel's president has thrown Prime Minister Benjamin Netanyahu a political lifeline, asking him to try to form a government after he failed to secure a clear election victory twice in six months.

The inconclusive ballot on September 17 left had Netanyahu weakened and his right-wing Likud party in second place, with 32 seats versus 33 for former armed forces chief Benny Gantz's centrist Blue and White party in the 120-member parliament.

But neither leader was able on his own to put together a coalition with a ruling majority, or reach a power-sharing deal for a unity government between their two parties.

Read: Israel's Netanyahu clings to power as coalition talks loom

Facing stalemate, President Reuven Rivlin tasked Netanyahu on Wednesday with what could be an impossible mission, leaving Gantz waiting on the sidelines to see whether he will get a chance should Israel's longest-serving leader not succeed.

As things stand now, Netanyahu still has no clear path to a fifth term after a decade in power — and there's also no obvious road to victory for political newcomer Gantz.

Why did Rivlin choose Netanyahu?

Under Israeli law and after consultations with leaders of parties that won parliamentary representation, the president picks a legislator the head of state deems has the best chance to put together a government.

In tapping Netanyahu, Rivlin noted that 55 lawmakers in a right-wing and religious bloc had pledged support for the Likud chief versus 54 for Gantz in a grouping that includes 10 Arab members of parliament who said they would not serve in any government.

Talks launched on Tuesday between Netanyahu and Gantz on forming a unity administration, possibly with a rotating premiership, went nowhere.

What's next?

Netanyahu now has 28 days to announce whether he has assembled a governing coalition. He can ask Rivlin for a 14-day extension, if necessary.

The canny politician, dubbed "the magician" and "King Bibi" by his supporters, may not even wait that long.

'You will never break our will': Palestinians react to Netanyahu's annexation pledge

Looking at a static political lineup and with no obvious way out of the deadlock, Netanyahu has already played down his chances of coalition-building, touching off speculation that he will "return" his presidential mandate soon.

That could set up a scenario — one that some political pundits say Netanyahu could actually be counting on — where Rivlin turns to Gantz who, lacking the numbers in parliament, fails as well.

"My inability to form a government is slightly less than that of Gantz," Netanyahu said, accepting the task, and repeating a call for a unity government with Blue and White.

What if both men fail to form a government?

With little appetite among Israeli voters for a third trip to the polls in less than a year if no government emerges, public pressure could grow for Netanyahu and Gantz to compromise and join forces.

Asserting they are giving the people what they want, they could feel free to walk back promises they made to their respective allies — pledges that served as obstacles to a unity administration, some political pundits said.

Under that game plan, Gantz would be able to abandon his vow not to sit in a government with a prime minister facing possible charges in three corruption cases.

Netanyahu, who denies the bribery and fraud allegations, could break up his current alliance with ultra-Orthodox Jewish parties. Gantz opposes that partnership, saying he seeks a liberal, or secular, government.

What if 'unity' proves impossible?

Wildcard Avigdor Lieberman, whose far-right Yisrael Beitenu party won eight seats in parliament, could always come off the fence. But citing policy differences with Likud's ultra-Orthodox backers and Blue and White's left-wing allies, he has shown no sign of budging.

So, it'll likely be election time — again.

That could leave Netanyahu in an even weaker political position, a two-time failure in doing what used to come easy to him: building a coalition.

But it would also leave him in his current role of caretaker prime minister, with any new vote months away.

Netanyahu would retain a commanding position while continuing to meet world leaders and hammer home a campaign message highlighting close ties with Israel's main U.S. ally and dangers posed by arch-foe Iran.

As prime minister, he would also be under no legal obligation to resign if formal charges are filed in the corruption cases.

At pre-trial hearings next Wednesday and Thursday, Netanyahu's lawyers will try to persuade Israel's attorney not to press on with his stated intention to indict him.