But Mark Regev, the Israeli government spokesman, declined comment on the report, which also said Netanyahu's negotiator had rejected Mitchell's request at a meeting in London on Monday.
Relations between the US and Israel have been soured by Washington's repeated calls for a freeze on settlement expansion, a move Israel has so far refused.
The US said it was "dismayed" over the approval to expand the Gilo settlement and sharply criticised the ongoing evictions and demolition of Palestinian homes.
Robert Gibbs, the White House press secretary, said in a statement: "At a time when we're working to relaunch negotiations, these actions make it more difficult for our efforts to succeed."
Regev repeated Israel's refusal to include areas it annexed to Jerusalem as part of any accommodation of calls by Barack Obama, the US president, for "restraint" in West Bank settlement growth.
"Prime Minister Netanyahu, in order to get the peace process back on track, is willing to adopt the policy of the greatest possible restraint concerning growth in the West Bank - but this applies to the West Bank," Regev said.
"Jerusalem is Israel's capital and will remain as such," he said, stating an Israeli position not recognised by world powers and contested by Palestinians who want to establish a state with East Jerusalem as its capital.
Al Jazeera's Jacky Rowland in Jerusalem said: "What we are seeing is Israel's strategy of trying to differentiate between East Jerusalem and the rest of the occupied West Bank.
"We have seen the government repeatedly claim that Jerusalem is its so-called united capital and the government said just today that whereas it planned to exercise what it called maximum restraint in the West Bank, it claimed that Jerusalem was a different case."
The plan for the housing units was cleared at a local level in April and passed by a committee of the interior ministry on Tuesday, Rowland said.
"It [Gilo] is one of these Jewish settlements across the green line in occupied Palestinian land which is attached to Jerusalem basically as a way of Israel trying to strengthen its grip on the capital, and literally create 900 more facts on the ground," she said.
Israel rejects the international description of Gilo as a settlement and says it is a neighbourhood of Jerusalem.
Tel Aviv's refusal to halt settlement construction in the Occupied Territories has stalled any hopes of resuming peace talks between the Palestinians and Israelis.
Al Jazeera's Nour Odeh, reporting from the West Bank city of Ramallah, said the announcement would be "very disappointing" for the Palestinians, who have set a complete freeze on settlement expansion as a precondition for resuming peace talks.
"This announcement in many ways validates the Palestinian argument that you have an Israel government that is not committed to the two-state solution; that does not even recognise that East Jerusalem is occupied land," Odeh said.
The Palestinians swiftly condemned the approval of the housing units, saying Israel is "not interested in peace".
Nabil Abu Rudeineh, the spokesperson of the Palestinian president, told Al Jazeera: "We condemn this step as it sends a clear message that Israel is not interested in peace and that it wants to ensure the failure of international efforts to reach peace and protect the two-state solution.
"Israel wants, through its actions, to secure the invalidity of establishing an independent Palestinian state. The international community's continued acceptance of these Israeli measures threatens stability in the region and the foundations of peace we seek."
The West Bank-based Palestinian Authority has expressed frustration at Israel's refusal to concede in order to get peace talks back on track and on Sunday said they would take steps to get the UN to back their right to an independent state.
While calling on Israel to show restraint in settlement expansion as a gesture of goodwill, the US has also urged Mahmoud Abbas, the Palestinian president, to drop his demand for a total freeze.
Netanyahu has offered a temporary restriction on projects that have not already started in the West Bank, but Abbas says this is insufficient and that it does not include areas Israel annexed to Jerusalem.