The talks at the White House were held behind closed doors
Israeli PM Benjamin Netanyahu has held talks with US President Barack Obama - their first meeting since a row over plans to build homes in East Jerusalem.
They held two meetings at the White House in what the Israelis said was a "good atmosphere".
Mr Netanyahu had warned earlier that Middle East peace talks could be further delayed by Palestinian demands for a freeze on settlement building.
The Palestinians said Mr Netanyahu's policy was stalling the peace process.
Meanwhile, it emerged on Tuesday evening that the Jerusalem municipal government had just approved the building of 20 new apartments for Jews on the site of an old hotel in the Sheikh Jarrah area of East Jerusalem.
The news drew criticism from chief Palestinian negotiator Saeb Erakat, who said in a statement that Israel was "digging itself into a hole".
An Israeli Likud MP, MK Yariv Levin, was quoted as saying the building approval was the "translation of Netanyahu's words into deeds" - referring to the PM's assertion on Monday of Israel's "right to build" in Jerusalem.
A White House official told the BBC that Mr Netanyahu and Mr Obama had first met for about 90 minutes.
He added that the US president later went to his residence, but Mr Netanyahu requested another meeting and the two leaders spent another 30 minutes together.
The Israeli prime minister's office said there was "a good atmosphere" during the talks.
But the White House had no immediate comment on their content. In a break with convention, reporters were not invited to witness the pair shake hands at the start of their discussions.
It was a pointed contrast with the traditional public welcome for Israeli leaders at the White House, the BBC's Steve Kingstone in Washington reports.
Our correspondent says that for the Americans it reflects an uncomfortable fact: that in the wake of a full-scale diplomatic row, Mr Netanyahu came to Washington offering no obvious concessions.
Paul Wood, BBC News, Jerusalem
The final building permits for the Shepherd Hotel development in East Jerusalem came through just a few hours before Benjamin Netanyahu's meeting with President Obama. Mr Netanyahu has supposedly put in place a procedure - involving the vetting of announcements by senior officials - to prevent such embarrassments. Clearly it is not working.
Israeli officials will no doubt, once again, try to portray this as a low-level bureaucratic decision which has no relationship to the high diplomacy between Israel and the US. Since the US has protested about this project, small as it may be, before, that is not really credible.
This may have come about - as with the Ramat Shlomo announcement - because right-wingers are seeking to make themselves look good to their own supporters by making Mr Netanyahu look bad. Conversely, sources in the Jerusalem municipality have accused the Israeli left of publicising the new building permits in order to "rekindle the situation on the ground".
The Israeli prime minister's officials spent a great deal of time explaining the realities of coalition politics here to Joe Biden's people when the Ramat Shlomo debacle happened during the vice-president's visit. It looks as if it is time for those same explanations to be rolled out again.
At an earlier meeting with US congressional leaders, Mr Netanyahu described the Palestinian demands on a construction freeze as "illogical and unreasonable".
"It could put the peace negotiations on hold for another year," he said.
Last week Mr Obama said the approval of plans for 1,600 homes in Ramat Shlomo was not helpful to the peace process. But on Monday, Mr Netanyahu reasserted Israel's "right to build" in Jerusalem.
Nearly 500,000 Jews live in more than 100 settlements built since Israel's 1967 occupation of the West Bank and East Jerusalem. They are considered illegal under international law, although Israel disputes this.
The Palestinian Authority is furious at Israel's insistence on building on occupied territory. It sees it as a serious stumbling block to the resumption of talks, which have been stalled for more than a year.
"Netanyahu's policy is the one that is obstructing the return to negotiations," Nabil Abu Rdainah, a senior aide to Palestinian President Mahmoud Abbas, told Reuters news agency in the West Bank city of Ramallah.
Mr Obama has largely refrained from commenting publicly on the announcement of new construction in East Jerusalem, which came while Vice-President Joe Biden was visiting Israel two weeks ago.
Instead, Secretary of State Hillary Clinton, along with Mr Biden and several top aides, has repeatedly criticised the Israeli government for jeopardising the indirect "proximity talks" being mediated by US special envoy George Mitchell.
In a speech to an influential pro-Israeli lobby group on Monday, Mrs Clinton demanded that Israel move to restore confidence in the peace process, not least by extending the 10-month suspension of new building in the West Bank to include East Jerusalem.
She told the American Israel Public Affairs Committee (Aipac) members that the continued expansion of Jewish settlements undermined "mutual trust and endangers the proximity talks that are the first step toward the full negotiations that both sides want and need".
"It exposes daylight between Israel and the United States that others in the region hope to exploit," she added.
In his speech to Aipac on the same day, Mr Netanyahu said: "The Jewish people were building Jerusalem 3,000 years ago and the Jewish people are building Jerusalem today.
"Jerusalem is not a settlement. It's our capital."
The BBC's Paul Wood in Jerusalem says that what details there are of the talks in Washington suggest that the US and Israeli leaders are clearly down to hard negotiations, and the stage is set for a historic test of wills.
On the Israeli side, there is a neurosis about the important relationship with the US, our correspondent says.
But the US will also be concerned that when there is daylight between the two countries, it points to trouble in the region.
The last thing the US wants is for this to turn into some sort of problem that would encourage Israel's enemies there, our correspondent adds.
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: Municipality approves the building of 20 new apartments on the site of an old hotel
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