Israeli Prime Minister Benjamin Netanyahu has said he "regrets" warning "the Arabs are voting in droves" during last week's elections.
He said he had not meant to offend Israeli Arab voters.
In a Facebook message directed at supporters on election day, he warned that "right-wing rule is in danger" as left-wing organisations were bringing Arabs to vote "in buses".
The Joint List alliance of Arab-dominated parties rejected the apology.
The prime minister had feared his voters would stay at home, but won against expectations.
Mr Netanyahu now says he hopes to form a new governing coalition within two or three weeks.
Apologising for his comments he said: "I know the things I said a few days ago hurt some Israeli citizens.
"My actions as prime minister, including massive investment in minority sectors, prove the exact opposite.
"I think, similarly, that no element outside the state of Israel should intervene in our democratic processes."
Ayman Odeh, leader of the Joint Arab List - an alliance of Israeli Arab-dominated parties that united for the first time and secured 13 seats at last week's election, told Israel's Channel 10: "We do not accept this apology.
"It was to a group of elders and not to the elected leadership of Israel's Arabs. I want to see actions, how is he going to manifest this apology? Will he advance equality?"
Mr Netanyahu's comments on election day drew criticism from the White House, which said it was "deeply concerned" by "divisive rhetoric" that sought to marginalise Israeli Arabs.
Ahead of the vote, Mr Netanyahu also said he would not allow the creation of a Palestinian state if re-elected.
His centre-left opposition, the Zionist Union, had promised to repair ties with the Palestinians and the international community.
Mr Netanyahu has since watered down this position in an interview with MSNBC.
But White House adviser Denis McDonough said on Monday that "we cannot pretend that these comments were never made."
Israeli Arabs, descendants of the 160,000 Palestinians who remained after the State of Israel was created in 1948, represent about 20% the Israeli population.