U.S. Department of State spokeswoman Jen Psaki warned Palestinian President Mahmoud Abbas on Monday against dissolving the Palestinian Authority, saying “those kinds of extreme measures would have grave implications” on the relationship between the U.S. and the Palestinians.

“A great effort has been made in the last few years to build Palestinian institutions, including with U.S. financial aid,” she said. “Dissolving the Palestinian Authority is not in the interest of the Palestinians … and will have implications on our relationship and our assistance.”

Abbas told several Knesset members last Wednesday that if the peace talks remained deadlocked he would ask Israel to assume responsibility for running the West Bank. “You won’t need tanks,” he said. “Just send in a minor officer and we’ll hand over the keys.”

In a meeting Thursday with U.S. envoy Martin Indyk and Israeli negotiators, Palestinian chief negotiator Saeb Erekat confirmed that Abbas was dead set on dissolving the PA.

A senior Israeli official with knowledge of the events at Thursday’s meeting said that unlike previous threats, Ereket’s message was considered serious and severe.

“The mood on the Palestinian side is extremely negative,” said the official. “They are seriously considering drastic measures. As opposed to the past, we no longer take lightly Palestinian declarations about giving back the keys.”

For his part, Prime Minister Benjamin Netanyahu commented Monday evening on the Palestinian threats. “Yesterday the Palestinians talked about dismantling the authority, and today they talk about unifying with Hamas. They should make up their minds if they want dismantling or unification,” he said.

According to Netanyahu, “When they want peace, let us know.”

This Saturday, Abbas is due to convene the Fatah Central Committee – the second most important Palestinian body regarding policy decisions. The committee last met in 2009, when Abbas’ term expired and had to be extended by a special PLO decree due to the split with Hamas after the group’s 2007 coup in Gaza.

Israeli and Palestinian officials said the meeting is expected to consider whether to extend negotiations with Israel, or whether to abandon the peace talks once and for all. A key issue up for discussion will be the possibility of dissolving the PA. Possible unilateral steps at UN bodies will also be discussed.

The senior Israeli official with knowledge of Thursday’s meeting said it lasted five hours but didn’t yield any breakthroughs.

“The gaps between the two sides are very big,” the official said. “We did not progress at all during the meeting and there isn’t much time left to secure a deal.”

The official said the Palestinians are demanding that Israel release a fourth batch of prisoners – a group that would also include 14 Israeli Arab prisoners. They also want to continue the negotiations with a serious, three-month discussion about the borders of a Palestinian state, and impose a full freeze on settlement construction in the West Bank and East Jerusalem. Israel agrees to few of these demands.

In just one week, on April 29, the nine-month period set for the talks will be over. Meetings between Israel and the Palestinians, mediated by U.S. envoy Martin Indyk, will continue on Tuesday. Officials on both sides predict that U.S. Secretary of State John Kerry, who hasn’t visited the region for weeks, will return to Israel before that date in an attempt to salvage the negotiations.

Psaki said that at this stage Kerry has no visit scheduled. She said the possibility of a visit would be reviewed daily, depending on whether it could have any bearing on the talks.

“We are still looking for a formula or a mechanism to move forward and extend the talks. We hope the parties can reach an agreement as soon as possible,” Psaki said.