The Likud Party on Tuesday tabled an amendment to the election law so that the minimum time allowed to hold snap elections to be cut down from 90 to 45 days.
There is a broad cross-party consensus for the move with Yisrael Beytenu having already suggested the change and the Blue and White party reportedly considering the change positively.
As the political stalemate continues and a third election campaign within a year seems inevitable, Likud MK Miki Zohar, who tabled the amendment to the law, said that in the interest of the country, elections should be held as soon as possible after they were announced.
The amended law would also cancel the vacation day given to Israelis on Election Day in an effort to reduce the cost to the local economy.
Meanwhile, some on the right have expressed a desire to avoid a third round of elections, arguing it could cost their camp in votes.
Among those voices was New Right leader Ayelet Shaked, who said Tuesday: "There is a real danger that the next elections will result in a 61-member bloc for the center-left parties supported by the [predominately Arab Joint List]."
Shaked said dragging the country into another election was irresponsible in light of the challenges Israel is facing.
"It is a matter of willingness to reach agreements," Shaked said, referring to the abortive coalition talks held after the April and September votes.
Likud minister Ze'ev Elkin, speaking at the same Sderot memorial event for late prime minister YItzhak Shamir, said: "I hope there is still a chance to form a viable coalition."
Yisrael Beytenu leader Avigdor Liberman said both major parties - Likud and Blue and White - are equally to blame for the political crisis.