In a strongly worded statement, the Quartet condemned Israel's announcement last week of planning permission for 1,600 new homes in East Jerusalem, occupied by Israel since 1967.
After the announcement, the Palestinians declared they could not begin US-brokered indirect, or "proximity", talks with the Israelis.
"The Quartet urges the government of Israel to freeze all settlement activity, including natural growth, dismantle outposts erected since March 2001 and to refrain from demolitions and evictions in East Jerusalem," Mr Ban said.
"Recalling that the annexation of East Jerusalem is not recognised by the international community, the Quartet underscores that the status of Jerusalem is a permanent status issue that must be resolved through negotiations between the parties, and condemns the decision by the government of Israel to advance planning for new housing units in East Jerusalem."
Kim Ghattas, BBC News, Moscow
Hillary Clinton seems to believe that the spat over settlements with Israel might produce something positive. In a BBC interview she appeared to concede that escalating the tone with the Israelis had been a risk but she said it was "paying off".
She added she believed there would be a "resumption of the negotiating track soon". In other words, pressure on Israel is working.
But the pressure will have to continue if there are to be concrete results. Israeli officials are already pushing back.
Mrs Clinton said Benjamin Netanyahu had committed to peace and she made clear she expected him to deliver. She added it was his responsibility to bring the whole of his government, a right-wing coalition, on board.
Mr Ban stated the goal of an Israeli-Palestinian peace agreement - including a Palestinian state - within two years.
Palestinian chief negotiator Saeb Erekat welcomed the Quartet statement and urged the creation of a "surveillance mechanism installed by the Quartet to make sure that Israel does effectively halt completely all settlement activity in the West Bank and East Jerusalem".
The pressure is now on the Israelis to offer concessions that will convince the Palestinians to participate in talks, says the BBC's Richard Galpin in Moscow.
But Israeli Foreign Minister Avigdor Lieberman said the Quartet timetable was unrealistic and ignored "the last 16 years of Israeli attempts" at negotiating with the Palestinians.
He said Israel had made many "significant gestures" and it was up to the Palestinians to "prove that they are really interested in negotiations".
Mrs Clinton told the BBC she hoped to see the resumption of indirect talks in the near future, eventually moving to direct talks.
Asked whether she had taken a risk in escalating the tone with Israel, Mrs Clinton said: "I think we are going to see the resumption of the negotiating track, and that means that is paying off, because that is our goal."
West Bank clashes
Events on Friday in the Middle East highlighted the difficulties the Quartet faces.
Palestinians in the West Bank town of Hebron threw stones at Israeli security forces, who fired tear gas in return.
Protesters and Israeli forces clash in the West Bank
And a rocket was fired into southern Israel from the Gaza Strip. It caused no injuries, but came a day after a rocket attack killed a Thai agricultural worker when it hit an Israeli kibbutz.
Israeli aircraft attacked up to six targets in Gaza overnight but there were no reports of any serious casualties.
On the eve of the Quartet meeting, Mr Netanyahu informed Mrs Clinton of new confidence-building measures that could be taken, but no details have been given.
It is likely this means a goodwill gesture by the Israelis, like the release of Palestinian prisoners, says the BBC's Kim Ghattas, travelling with Mrs Clinton.
Enough progress was apparently made in their telephone conversation for George Mitchell, Washington's Middle East envoy, to travel to the region this weekend.
Mr Netanyahu is to visit Washington next week for further talks with Mrs Clinton.
At the heart of the conflict are disputes over the status of Jerusalem, the borders of Israel and a future Palestinian state and the fate of Palestinian refugees.
POINTS OF TENSION IN JERUSALEM
1 Gilo: 850 homes approved for publication and planning objections in Nov 2009
2 Pisgat Zeev: 600 homes approved for publication and planning objections in Jan 2010
3 Sheikh Jarrah: Several Palestinian families evicted in past 18 months to make way for Jewish settlers after court ruled in ownership dispute
4 Ramat Shlomo: 1,600 homes approved for publication and planning objections in Mar 2010
5 Silwan: Demolition orders on 88 Palestinian homes built without difficult-to-get permits - Israel planning controversial renewal project
6 West Bank barrier: Making Palestinian movement between West Bank and Jerusalem harder - Israel says it's for security
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