Israeli President Shimon Peres gave Netanyahu six weeks to cobble together a coalition.
Netanyahu, 59, immediately called for a broad, national unity coalition with centrist and left-wing partners, but there was no sign that his rivals would accept, and Netanyahu may have no alternative but an alliance with far-right and ultra-religious parties.
"I call on Kadima chairwoman Tzipi Livni and Labor Party chairman Ehud Barak, and I say to them, let's unite to secure the future of the State of Israel," Netanyahu said at a news conference also attended by President Peres.
Livni, 50, leader of the centrist Kadima, has suggested she would rather be in opposition than join a government led by Netanyahu, who was prime minister in the late 1990s. The Kadima party narrowly defeated Likud in the Feb. 10 election, but Netanyahu has the support of religious and right-wing parties in the Israeli parliament.
The choice of Netanyahu was essentially cemented Thursday when Avigdor Lieberman, who heads the hawkish Yisrael Beiteinu party, endorsed him.
Lieberman's party, which based its campaign on requiring Israel's Arab citizens to swear loyalty to the Jewish state or lose their citizenship, came in third place in the election, after Kadima and Likud. That essentially allowed him to determine whether Netanyahu or Livni would be able to muster the backing of a majority in parliament.
Minutes before the news came out that the Likud leader would be asked to form a government, Livni said what was being proposed was a government "without political vision, a government with no values," reported the BBC. "I will not be a pawn in a government that would be against our ideals," she said.
Likud more than doubled its seats in the election in which Israeli security was the paramount issue. But there was no clear winner. With 27 seats in the 120-seat Knesset, Netanyahu ended up one seat behind Kadima.
One of the main points of contention between the two parties is how to handle the Palestinian territories. Livni favors more talks and the creation of a separate state for the Palestinians; Netanyahu says he does not want Israel to rule the Palestinians, but says they should not be allowed things he considers a threat to Israeli security, such as an army or control of airspace or the Jordan Valley.
Meantime, sporadic violence continued in Gaza in the absence of a long-term cease-fire between Israel and Hamas. Militants fired mortar shells at an Israeli patrol along the Gaza-Israel border Friday, Israeli defense officials said, and the troops returned fire. There were no injuries reported.