In his first public remarks on what Israeli commentators called his most serious crisis with Washington since taking office a year ago, Netanyahu told his cabinet at its weekly meeting, after a reprimand by Hillary Clinton, the US secretary of state, "not to get carried away and to calm down".
"There was a regrettable incident here, that occurred innocently ... It was hurtful and certainly it should not have happened"
Israeli prime minister
"There was a regrettable incident here, that occurred innocently ... It was hurtful and certainly it should not have happened," he said.
Netanyahu added that he had appointed a team of senior officials "to pinpoint the sequence of events, to ensure procedures will be in place to prevent these kinds of incidents in the future".
Sherine Tadros, Al Jazeera's correspondent in Jerusalem, said that the announcement had only served to increase tensions in the occupied West Bank and East Jerusalem.
"Things have been incredibly tense here following the announcement that there will be more Jewish housing units built on occupied Palestinian land," she said.
"I think that Palestinians are not just concerned once again that their presence in Jerusalem will be diminished and that Israel is trying to 'cleanse' them from the Holy Land, but also by the fact that these announcements came right under the nose, if you like, of the US and [that] the international community is doing nothing to stop it."
Clinton called Israel's move "insulting". Others, including the Palestinians and the Middle East diplomatic Quartet, condemned the plans for building new settlement homes.
However, Biden told the Reuters news agency on Friday he believed Netanyahu was sincere in seeking a deal to give the Palestinians a state.
Clinton said Israel was putting its US ties at risk by making unilateral announcements.
She told Netanyahu in a telephone call on Friday that he must act to repair the relationship and show his commitment to an alliance which, she reminded him, was key to Israel's security in a hostile region.
Clinton accepted that Netanyahu was taken by surprise by the housing approval granted on Tuesday by his interior ministry, which is run by the pro-settler religious Shas party, but she said the prime minister was still responsible for it.
Michael Oren, Israel's ambassador to the United States, was summoned to the State Department on Friday to meet Jim Steinberg, the deputy secretary of state, in a further sign of US displeasure at the housing announcement.
In Washington, the Anti-Defamation League (ADL), which lobbies for Israel with US legislators, called Clinton's remarks on the diplomatic debacle a "gross over-reaction".
ADL's Abraham Foxman said: "We are shocked and stunned at the administration's tone and public dressing down of Israel.
"We cannot remember an instance when such harsh language was directed at a friend and ally of the United States. One can only wonder how far the US is prepared to go in distancing itself from Israel in order to placate the Palestinians."
Barack Obama, the US president, is seeking better US relations with the Arab world, which backs the Palestinians, as he seeks to bolster alliances in the oil-producing hub, notably against Iran that is suspected of developing nuclear bombs.
Aides to Mahmoud Abbas, the Palestinian president, said he was waiting to meet George Mitchell, Obama's peace envoy, when he returns to the region in the coming days before deciding whether to maintain his week-old commitment to starting "proximity talks" with Netanyahu via US mediators.
The Israeli settlement issue has been one of the main issues blocking the Israeli-Palestinian talks.
Palestinians have always demanded that talks should not start without Israeli commitment to a complete settlement freeze. Meanwhile the Israelis stress that they are sincere in their willingness to reach a solution with the Palestinians and that the Palestinians’ approval to sit on the table should not come with strings.