The envoy also met this week in Ramallah with Palestinian Authority President Mahmoud Abbas, as well as with with Israeli President Reuven Rivlin, Israeli military officials, Palestinian children in a West Bank refugee camp and Jordan's King Abdullah II in Amman.
The policy would have to be "agreed-upon for us, of course, not just for the American side", he said.
Israeli Prime Minister Benjamin Netanyahu and Jason Greenblatt, President Donald Trump's adviser on global relations, "made progress" on the issue of West Bank settlement construction, the Prime Minister's Office said.
Netanyahu said that he will insist on building a new settlement for the residents of the illegal outpost of Amona, which was evacuated by Israeli authorities in February after the Supreme Court found it was constructed unlawfully on private Palestinian lands.
Netanyahu and Greenblatt will meet for more talks later on Thursday, before the US envoy returns to Washington.
The Yesha Council, the main Israeli settler organization, said it was believed to be the highest level official meeting ever for the organization with a US administration.
During Greenblatt's second meeting with Netanyahu on Thursday, which lasted three hours, the two politicians failed to reach a concrete agreement. "Those discussions are continuing between the White House and the Prime Minister's Office", it adds.
At the same time the "positive discussion" was also focused on "advancing a genuine and lasting peace between Israel and the Palestinians that strengthens the security of Israel", said the statement. Palestinians want the West Bank and East Jerusalem for their own state, along with the Gaza Strip. Some 385,000 Israeli settlers live in the West Bank that is home to 2.8 million Palestinians. Israel's ambassador to the United States, Ron Dermer, was present for most of the meeting, and the most significant part of the conversation dealt with the attempt to formulate understandings on construction in the settlements. Another 200,000 Israelis live in East Jerusalem. "I'm looking at two-state and one-state..." Israel disagrees, citing historical and political links to the land, as well as security interests.