“One who is afraid of votes in a ballot box will eventually see stones thrown in the streets,” the president, Reuven Rivlin, said as he ceremonially received the certified results of last week’s election. Later, standing next to Mr. Netanyahu, he described “a difficult election period” in which “things were said which ought not to be said — not in a Jewish state and not in a democratic state.”

Mr. Netanyahu apologized this week for expressing concern in a video about Arab turnout, remarks that the White House, world leaders, American Jews and many inside Israel had condemnedas race-baiting and fearmongering. As he accepted the mandate for a fourth term, the prime minister did not revisit the uproar over those remarks or directly address his pre-election disavowal of support for a Palestinian state, which together have drawn unrelenting criticism from President Obama and his aides.

“Our hands are held out in peace towards our Palestinian neighbors, and the people of Israel know that true peace will only be guaranteed if Israel remains powerful, both in spirit and in strength,” Mr. Netanyahu said Wednesday.

Prime Minister Benjamin Netanyahu and Israel’s president, Reuven Rivlin, on Thursday.

MENAHEM KAHANA / AGENCE FRANCE-PRESSE — GETTY IMAGES

“We greatly appreciate, and will keep our pact with, the closest of our friends, the United States of America,” he continued, “and we will nonetheless continue to act to prevent the unfolding deal with Iran, an agreement which puts in danger us, our neighbors, the world.”

Mr. Netanyahu now has up to six weeks to form a governing coalition, an internecine process of deal-making over ministerial posts and policy positions. He is widely expected to do so with six rightist and religious parties that together won 67 of Parliament’s 120 seats, though some Israeli analysts said the crisis in relations with Washington had increased the pressure on him to form a unity government with the center-left Zionist Union or the centrist Yesh Atid, or both.

Senior members of Mr. Netanyahu’s Likud party and the heads of the ultranationalist Jewish Home and Yisrael Beiteinu factions are all vying for the Foreign and Defense Ministries. Mr. Netanyahu has promised the finance position to Moshe Kahlon, a former Likud minister who formed Kulanu, a faction that focused on economic issues.

On Wednesday, Mr. Netanyahu vowed that the government’s first budget would include steps to reduce the cost of housing and food and dismantle monopolies, tenets of Mr. Kahlon’s campaign.

Mr. Rivlin, a Likud member whose term as president has been marked by outreach to Israel’s 1.7 million Arab citizens and residents, said Mr. Netanyahu should make the government “as inclusive as possible.”

Alongside improving relations with the United States, other “critical missions” for the new government, according to Mr. Rivlin, include returning stability to the political system to avoid another early election, and “healing the wounds, mending the painful rifts, which have gaped open in the past years, and widened further in the course of this recent election.”