Netanyahu faces a deadline imposed by Shimon Peres, the Israeli president, to form a cabinet by April 3.
The two parties are poised to secure agreements with other parties in order to achieve a majority within Israel's 120-seat parliament.
Netanyahu, who served as prime minister from 1996 to 1999, is likely to form a cabinet dominated by conservatives since both the Kadima and Labour party have refused to join his government.
Al Jazeera's Mike Hanna in Jerusalem said: "Seeing how the government is set up and how the US administration is beginning to position itself, combined with the demands of the Palestinians between these factors, it's very difficult to see anything but a long period of wrangling and anger as well as little progress in peace negotiations.
"The important point to note is that Yisrael Beiteinu agrees to a two-state solution, perhaps different from the kind of two-state solution that Palestinians might envisage.
"Lieberman's wants a pure Jewish state and anyone who doesn't pledge an oath of allegiance to Israel must be deported to another state alongside, which he sees as a Palestinian state," he said.
Lieberman's appointment as foreign minister raised concerns that Israel's international ties will be harmed.
Lieberman has been accused of being a racist demagogue because of his plans to require loyalty oaths from Israeli Arabs as a pre-condition for gaining citizenship.
A narrowly based government and a prominent role for Lieberman could put Netanyahu on a collision course with the administration of Barack Obama, who has pledged to pursue an Israeli-Palestinian peace deal.
Yisrael Beiteinu, which won 15 seats in the 120-member parliament, wants to trade land where Israeli-Arab citizens live in exchange for illegal Jewish settlements in the West Bank in any peace deal with Palestinians.
Despite the deal with Lieberman's party, Netanyahu's deputies are continuing efforts to form a broad-based coalition by winning support from Tzipi Livni, the outgoing foreign minister and Kadima leader.
Livni has demanded Netanyahu to commit to US-backed talks with Palestinians for a two-state solution, as a condition for joining any government.
She also demanded a power-sharing arrangement in exchange for joining a government alongside him.