This is not recognised by the international community, with the east of the city considered occupied territory.
Palestinians hope to establish their capital in East Jerusalem, as part of a two-state peace deal with the Israelis.
They say Israel uses settlement and demolition orders to try to force them from the area.
'No credibility'
The project in question concerns a block of 20 apartments in the Sheikh Jarrah district of the city.
Israeli officials said the US State Department summoned Ambassador Michael Oren last week and told him that the construction should not go ahead.
There was no immediate comment from the US.
But Israel has come under pressure from the Obama administration to freeze settlement activity on land that Palestinians want for a future state.
Palestinians say peace talks cannot proceed until settlement activity halts.
A senior Palestinian negotiator, Saeb Erekat, said Mr Netanyahu's comments had further undermined efforts to re-start the peace process.
The decision to pursue this project, he said, reflected Israel's defiance of international calls for a halt to settlement activity.
"This undermines the efforts being exerted to revive the peace process and this undermines the credibility of those involved in making the peace process continue," he said.
About 268,000 Palestinians live in East Jerusalem, alongside 200,000 Israeli Jews.
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