Netanyahu's office said he ordered the inquiry late on Saturday after he met senior cabinet ministers.
The announcement embarrassed Biden, who was visiting Israel in a bid to revive Israeli-Palestinian peace negotiations.
Netanyahu has since apologised for what he called the bad timing of the announcement, but has given no sign he will cancel the construction orders.
Robert Gibbs, the White House spokesman, said the apology was merely a "good
"I think what would be an even better start is coming to the table with constructive ideas for constructive and trustful dialogue about moving the peace process forward," Gibbs told Fox TV.
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 on Sunday "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," he said.
Netanyahu said 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".
Hillary Clinton, the US secretary of state, had earlier told Netanyahu that his government was putting US ties at risk by failing to take action towards renewed Middle East peace talks.
Clinton accepted that Netanyahu was taken by surprise by the housing approval granted by his interior ministry, which is run by the pro-settler religious Shas party.
But she still held the prime minister responsible.
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.
|At the centre of the row is a move to build 1,600 new settler homes in East Jerusalem
"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."
Analysts say Netanyahu is split between striving for Middle East peace while not wrecking the fragile rightist coalition he heads.
Yossi Meckelberg from the Chatham House told Al Jazeera: "Netanyahu, if anyone wants to find an excuse for him, is leading an impossible coalition.
"He can stay in power only if he does nothing. If he does anything out of the routine management of government, he might find himself without a coalition."
The Palestinians and the Middle East diplomatic Quartet have 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.