Story highlights

NEW: Kerry meets for several hours with Israeli leader Netanyahu

A Palestinian official says talks with the U.S. are continuing

Kerry says he's hopeful that some issues "fleshed out" and "even resolved"

CNN  — 

America’s top diplomat continued his push Saturday for a Middle East breakthrough, saying amid talks with leaders of both Israel and the Palestinian Authority he feels the road toward peace “is real, not illusory.”

After meeting with Palestinian Authority leaders in Ramallah, West Bank, U.S. Secretary of State John Kerry said that progress had been made, but all sides still “have some very serious homework – all of us – to do.”

“I am confident that the talks we have had in the last two days have already fleshed out, and even resolved certain kinds of issues and presented new opportunities for others,” he said in a news conference with Palestinian negotiator Saeb Erakat.

He said that the “the next week” is key as to what happens next.

Kerry has floated a proposal based on five months of intensive consultations with Israelis and Palestinians since the resumption of the peace process last summer. As a result of those talks, he intends to test some of his ideas with the two sides’ leaders.

“It is an effort to provide agreed guidelines for a permanent status agreement; that is to say, a full and final peace treaty between the parties,” said a senior State Department official, who insisted these discussions would be substantive.

This is Kerry’s ninth trip to the region since taking over as secretary of State nearly a year ago.

He arrived in Tel Aviv on Thursday and immediately headed for Jerusalem, where he met for three hours with Netanyahu on Friday. Kerry then spent two days meeting with Palestinian leaders, including two meetings with Abbas.

Kerry then spent two days meeting with Palestinian leaders, including two meetings with Palestinian Authority President Mahmoud Abbas.

He held two meetings in as many days with Abbas, talks that the Palestinians’ official WAFA news agency described as intensive.

Afterward, presidential spokesman Nabil Abu Rudeineh said that Abbas had insisted that any agreement include the creation of an independent Palestinian nation with Jerusalem as its capital, a return to the borders pre-dating the 1967 Six-Day War, not legalizing Israeli settlements on Palestinian lands and the freeing of prisoners.

According to the WAFA report, Rudeineh also said that discussions with the United States would continue.

Kerry headed from the West Bank to Israel, where he met for more than 4½ hours late into the night with Netanyahu.

CNN’s Kareem Khadder contributed to this report.