Netanyahu was meeting separately with Foreign Minister Avidgor Lieberman, head of the ultra-nationalist Yisrael Beitenu, and with Naftali Bennett, of the far-right Jewish Home.
Media said he spent one and a half hours with Bennet in their first private talks for more than two weeks.
"The meeting lasted an hour and a half and the two agreed to work together to form the next government," news site Ynet reported.
Netanyahu's rightwing Likud party won Israel's March 17 general election but without a majority, and he has initially until April 22 to form a coalition.
If he needs more time he could by law request an additional two weeks to try and form a coalition.
If no government is found past that date, the president could task another party to form a coalition or the country can go to a fresh election.
Before heading to his meeting at Netanyahu's official Jerusalem residence, Lieberman told public radio he was going to discuss policy, not prospective portfolios.
"We want to sum up principles, on the death penalty for terrorists, the eradication of the Hamas regime," Lieberman said.
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"There are many things that we need to nail down."
Israel and the militant Islamic Hamas fought a 50-day war in Gaza last summer in which about 2,200 Palestinians and 73 Israelis were killed.
Hamas remains the de-facto power in the strip.
Ayelet Shaked, co-founder of the Jewish Home, said Bennett wanted Netanyahu to spell out the ideology of the future government and to scotch talk of a wall-to-wall coalition with the centre-left Zionist Union party.
"Its about partnership in government, serious partnership, real partnership," she told public radio.
"It has to be on the basis of the principles of the nationalist camp, not those of the left," she said.
"We need to know where this government is heading because we don't really understand."
According to public television, Netanyahu met secretly with Zionist Union chief Isaac Herzog, his main challenger in last month's election, to discuss the possibility of a national unity government.
Herzog has denied the report.
Netanyahu, who won a third consecutive term, and his fourth overall, has ruled out a unity government and said he intends to form a ruling coalition with his "natural" rightwing and ultra-Orthodox partners.