JERUSALEM — Israel’s president on Wednesday officially handed Prime Minister Benjamin Netanyahu the task of forming a new government, saying its first priority was to repair relations with the United States and indirectly chiding Mr. Netanyahu for his Election Day warning that Arab citizens were flocking to polling places in “droves.”

“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 condemned as 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.