President Trump's Mideast adviser Jason Greenblatt is in Israel and will travel Tuesday to the West Bank to meet Palestinian President Machmoud Abbas.
Jason Greenblatt met first Monday with Israeli Prime Minister Benjamin Netanyahu.
He followed up Tuesday with a meeting with Palestinian President Mahmoud Abbas.
"I'm looking at two-state and one-state, and I like the one that both parties like".
Following the lengthy meeting, they issued a statement reaffirming "the joint commitment of both Israel and the United States to advance a genuine and lasting peace between Israel and the Palestinians that strengthens the security of Israel and enhances stability in the region".
Abbas is expected to visit the White House next month.
Greenblatt and Ron Dermer, Israel's ambassador to the US, were appointed by their leaders last month to reach an understanding between the two countries on settlement construction.
On Monday, Netanyahu and Greenblatt discussed Israel's settlement building "with the hope of reaching a formula that will aim to promote peace and security", the Israeli leader's office said.
Palestinian leaders have expressed interest in cooperating with the U.S. and Israel to improve the Palestinian economy, but have stressed that such efforts need to be a part of a plan to establish an independent Palestinian state.
"President Abbas assured Mr. Greenblatt that he is fully committed to creating an atmosphere that is conducive to making peace and would heighten his outreach efforts to the Israeli public", the consulate general announced.
Israel's premier has met with President Donald Trump's representative for global negotiations, reportedly about settlements in territory Palestinians claim for a state.
Greenblatt described his meeting with Abbas on Twitter as "positive" and "far-reaching".
Palestinians have demanded a settlement construction freeze for negotiations to renew.
"Netanyahu stuck to his promise to establish the new settlement", the senior official said. The settlement would be the first new government-approved settlement built in the West Bank in more than 25 years.