AMMAN, Jordan — U.S. Secretary of State John Kerry extended his stay in the Middle East on Friday to meet with President Mahmoud Abbas of the Palestinian Authority for the third time in four days, seeking to cajole Abbas to rejoin peace talks with Israel despite wariness from Palestinian political leaders.

Kerry arrived in Ramallah, the Palestinian Authority headquarters on the West Bank, Friday afternoon. His departure from Jordan was delayed for several hours as he spoke on the phone with Israeli and Palestinian officials.

The plans were announced after Kerry spent two hours in two sessions in Amman with the chief Palestinian negotiator, Saeb Erekat, who brought with him concerns expressed by leaders of the Palestine Liberation Organization in a late-night conclave Thursday.

Though Kerry and a team of diplomats and businessmen have spent months fine-tuning a broad package of economic incentives, security reassurances and political gestures in hopes of bring the two sides to the negotiating table, the border question seems to be among the major sticking points.

Abbas has for years insisted that any new talks be conducted on the basis of Israel’s borders before it seized Arab territories in the 1967 war, with minor adjustments. Prime Minister Benjamin Netanyahu of Israel has just as steadfastly refused.

To skirt around that apparent stalemate, Kerry’s team has tried to come up with a new framework, according to U.S., Israeli and Palestinian officials who have been involved in the process.

One possibility, they said, is that the United States will invite the two sides to the talks on the basis of the 1967 prewar borders and the recognition of Israel as a Jewish state, though Netanyahu and Abbas would not explicitly endorse those terms and might even oppose them while agreeing to negotiate.

Kerry’s ideas on how to approach economic, security and political issues won the backing Wednesday of a group of Arab League foreign ministers, but he has not yet convinced the PLO leadership.

After a stormy two-hour meeting here Thursday afternoon, several participants said it was “not enough.”

A spokesman for Netanyahu declined to discuss the diplomacy Friday. A leading lawmaker from his Likud Party, Tzachi Hanegbi, said in an interview on Israel Radio that “Israel can never return to the 1967 borders,” in which Jerusalem was divided, but that once negotiations start, “we must discuss everything.”

“We reject Palestinian dictates as preconditions for being willing to hold a dialogue with us,” Hanegbi said. “The Americans, it seems, understand the logic of this, and that is why their main efforts are invested in the Palestinians.”

He described the current situation as “the classic model of a tango,” adding, “One step forward, two steps back.”

President Barack Obama spoke by phone with Netanyahu on Thursday.

“The president encouraged Prime Minister Netanyahu to continue to work with Secretary Kerry to resume negotiations with the Palestinians as soon as possible,” the White House statement said.