Responding to reports that Israel might agree to suspend settlement activity for three months instead of enforcing a total freeze, Ian Kelly, a US state department spokesman, said: "I'm not going to say we're not willing to compromise."
Robert Gibbs, the White House spokesman, said the US was "optimistic about making progress" in Tuesday's meeting.
"This would be the largest area of land ever confiscated by Israel in one go since 1967"
Hatem Abdel-Qader, Palestinian minister
"I think the president has outlined the responsibilities of all," he added.
Despite the Barak-Mitchell meeting, Israel went ahead and approved the 50 new homes in a West Bank settlement on Monday.
The Israeli defence ministry on Monday presented to the supreme court plans to relocate settlers from an illegal outpost in the West Bank to a settlement north of Jerusalem.
And there are plans for another 1,400 housing units at the site, Israel's anti-settlement group Peace Now told the court.
Also on Monday, a spokesman for Israel's Civil Administration, which reports to Barak, said it had placed notices in the Arabic Al-Quds newspaper on Friday, inviting Palestinians who object to the move to expropriate land, to file appeals within 45 days.
"The land in question includes a strip along the shores of the Dead Sea that emerged over the years as the water receded due to shrinkage," the spokesman said.
According to the Al-Quds notices, the land to be expropriated totals 139 sq km and includes plots of land near the major West Bank settlement of Maale Adumim, the spokesman said, without giving further details.
The moves drew immediate criticism from Palestinians.
"This would be the largest area of land ever confiscated by Israel in one go since 1967," said Hatem Abdel-Qader, the Palestinian minister for Jerusalem affairs. "We will appeal against this decision."
Mahmoud Abbas, the Palestinian president, reiterated his stance that peace talks with Israel cannot resume until settlement construction comes to a complete halt.
"We won't accept the continuation of settlements," he said in the West Bank city of Ramallah.
Binyamin Netanyahu, the Israeli prime minister, has said he will not allow the building of new settlements but will allow construction in existing communities, under what Israel calls "natural growth".
His refusal to order a total freeze has given rise to rare public disagreements between his government and the Obama administration and even raised questions about whether the US will continue to actively support Israel at the UN.
But Gabriela Shalev, Israel's UN ambassador, said on Monday that the Obama administration had assured Israel that it would continue defending it at the UN.
"We were told explicitly [by the Americans] that there are no consultations and no discussions at all within the administration in this direction," Shalev told Israel's Channel Ten television.
Some 500,000 Israelis live among 2.5 million Palestinians in the West Bank and East Jerusalem, land Israel captured in the 1967 Middle East war.