Three far-right Israeli political parties joined forces late Wednesday, seeking to strengthen their hand in a coming election after a left-leaning alliance was announced earlier in the week.

Israel is gearing up for its third election in less than a year after neither Prime Minister Benjamin Netanyahu nor his centrist challenger Benny Gantz were able to form a majority government following two polls last year.

Whoever is tasked with forming a government will need to win the support of small parties, which can wield major clout in coalition negotiations.

Under Israel's system of proportional representation, parties may form joint electoral lists to boost their chances of being selected as coalition partners.

On Tuesday, Defence Minister Naftali Bennett's New Right party struck a deal with the National Union faction of Transport Minister Bezalel Smotrich.

On Wednesday night, just before the deadline for filing electoral lists, they were joined by the national religious Jewish Home party, led by Education Minister Rafi Peretz.

The trio will run under the name Yamina ("Rightward" in Hebrew).

Left out in the cold was Jewish Power -- the extreme-right party which many view as racist -- despite Netanyahu's reported push for them to be included in Bennett's alliance.

"I will not include on my electoral list someone who has in his living room at home a picture of a man who murdered 29 innocent people," Bennett wrote on Facebook Wednesday.

Video shot in Jewish Power leader Itamar Ben-Gvir's home in the flashpoint West Bank city of Hebron shows a photograph of Israeli settler Baruch Goldstein, who killed 29 Muslim worshippers with an assault rifle in 1994 before being beaten to death by survivors.

Ben Gvir, who lives in a Jewish settler enclave in the mainly Palestinian city, has been quoted as saying that the picture is there out of respect for Goldstein as a doctor he says saved Jewish lives.

Israeli media reported that Ben-Gvir had offered to take down the picture if Bennett allowed him into his alliance.

Data released by Israel's National Elections Committee on Thursday showed Jewish Power registered to run alone, with an optimistic 17 candidates on its list.

In the September election, Jewish Power failed to reach the threshold of 3.25 percent of the vote reqired to enter parliament. The other three far-right parties presented a joint list and won seven seats.

On Monday, the left-wing Labor-Gesher and Meretz parties announced they were joining forces for the next election.

Israel's four Arab-led parties registered as running together, as they did in September, as the Joint List.

A total of 30 lists were submitted, the National Elections Committee said.