His visit comes amid heightened tensions between Israel and Washington over the settlement announcement, made as Joe Biden, the US vice-president, visited Israel.
The expansion plan was seen as an insult to the US and frayed Israel's usually strong ties with Washington.
The Palestinians pulled out of planned so-called "proximity" talks after Israeli officials announced that the housing units would be built. They have demanded that all construction be stopped before they will return to negotiations.
In the aftermath there has been a flurry of diplomatic activity as major international powers have struggled to restart a peace process stalled for more than a year.
George Mitchell, the US envoy to the Middle East, met Netanyahu on Sunday, to present him with the official invitation to meet Obama on Tuesday and push for indirect talks between the Israelis and Palestinians.
He maintained pressure for renewed Israeli commitment to peace talks with the Palestinians, but also reassured Israel that the two countries enjoy an "unshakeable bond".
Jacky Rowland, Al Jazeera's Jerusalem correspondent, said: "What we're witnessing is really concerted efforts on the part of the international community to get some sort of peace process going again.
"It's been stagnant; it's been moribund for almost a year and a half now."
Ban Ki-moon, the UN secretary-general, was also in the region on Sunday, criticising Israel's blockade of the Gaza Strip during a visit to the Hamas-controlled territory.
Ban said that Israel's policy of closing off the territory is not sustainable and causes "unacceptable suffering".
Israel imposed a tightened blockade after the Hamas movement took full control of the coastal enclave in June 2007.
Ban told Gazans that "we stand with you" as he visited an area damaged by Israel's offensive 14 months ago.
Ban said families were living under "unacceptable, unsustainable conditions".
He saidd that it was "distressing" for him to see houses still damaged, with no reconstruction possible under the blockade.
The blockade has prevented the United Nations from completing housing projects, however, Ban pledged to continue providing aid to Gazans.
"My message to people of Gaza is this: the United Nations will stand with you through this ordeal," he said.
He also called for a prisoner exchange involving Palestinian prisoners and Israeli soldier Gilat Shilad who was captured in 2006.
The UN secretary-general's visit to Gaza followed a trip to the West Bank the previous day, where he reiterated demands that Israel end settlement building in Palestinian territory.
|The flurry of diplomatic activity comes amid violence on the ground in the West Bank [AFP]
"Let us be clear, all settlement activity is illegal anywhere in occupied territory and this must stop," Ban said, speaking at a joint news conference with Salam Fayyad, the Palestinian prime minister.
Ban emphasised the commitment of the so-called international Quartet of Middle East negotiators - comprised of the UN, the European Union, Russia and the US - to the establishment of a Palestinian state.
"The Quartet has sent a clear and strong message: we are strongly supporting your efforts to establish an independent and viable Palestinian state," Ban said.
He also met Israeli officials, including Shimon Peres, the Israeli president, as part of his trip.
But the moves on the diplomatic stage were overshadowed by violence on the ground in the West Bank.
Israeli troops shot dead two Palestiniansin the territory after they tried to stab a soldier at a checkpoint, the Israeli military said.
The deaths brought to four the number of Palestinians killed in the past two days in the West Bank.