Israel's announcement came as US Vice President Joe Biden was visiting Jerusalem.
In a statement, Mr Biden condemned the move.
He said it was precisely the kind of step that undermined the trust needed to make progress in peace negotiations between Israel and the Palestinians.
'I condemn the decision by the government of Israel to advance planning for new housing units,' Mr Biden said in a statement issued after he arrived 90 minutes late for a dinner with Israeli Prime Minister Benjamin Netanyahu.
UN Secretary-General Ban Ki-moon, who will visit Israel, the West Bank and Gaza after a meeting of Middle East peace mediators in Moscow next week, also criticised the plan.
'The secretary-general condemns the approval of plans for the building of 1,600 new housing units in East Jerusalem by the Israeli Ministry of Interior earlier today,' UN spokesman Martin Nesirky said in a statement yesterday.
