U.S. Secretary of State John Kerry, left, meets Palestinian President Mahmoud Abbas in the West Bank city of Ramallah on Dec. 12. (Brian Snyder/AP)

The Obama administration is struggling to convince Israel and the Palestinian Authority to accept a security arrangement that could leave Israeli troops stationed inside a future Palestinian state, on that state’s border with Jordan.

Neither side is on board with what people familiar with the proposals describe as a limited Israeli defensive presence along the Jordan River for a period of five to 15 years.

Secretary of State John F. Kerry returned to the region Thursday night — his second visit in a week — to try and convince them. Kerry is hoping for some public sign of progress as his first year as the chief U.S. diplomat draws to a close, and an unofficial April deadline for a peace agreement looms.

For Israeli Prime Minister Benjamin Netanyahu, limiting the number of Israeli troops in the Jordan Valley, and how long they can be there, would not guarantee safety.

For Palestinian Authority President Mahmoud Abbas, who has promised his people they would not see a single Israeli soldier on Palestinian land in a future state, any army presence would be too much.

Joint presentations to Netanyahu and Abbas last week by Kerry and retired Marine Gen. John R. Allen, the Obama administration’s special envoy, do not appear to have been well-received. Neither leader spoke in support of the proposals. Spokesmen and critics on both sides trashed the ideas in news media interviews, though they did not reject the proposals outright.

State Department spokeswoman Jen Psaki denied that Kerry’s speedy return to the region means that the talks are bogging down.

A generation of Israeli generals has considered the Jordan Valley a crucial eastern flank against a land invasion of the Jewish state from the east. But where they once worried about columns of Iraqi tanks, they are now more concerned about asymmetrical warfare from terror groups seeking to infiltrate the West Bank and use it as a platform to attack.

Since 1967, the valley has been under the control of the Israeli military, which operates checkpoints and bases. The area bristles with covert listening stations, radar sweeps and thermal- and night-vision cameras. On the mountain tops that rise steeply from the valley floor, Israel maintains a series of early-warning stations. Troops are on constant patrol along the river and the passes.

In a meeting last month with members of his Fatah political party, Abbas claimed that Israel wants to stay in the sparsely populated valley for another 40 years to maintain its profitable date palm groves, fish ponds and greenhouse farming.

“They say they need the Jordan Valley to protect themselves against the Iranian threat or whoever comes from the eastern border,” Abbas was quoted in local news reports as saying. “Rather, it is a matter of investment .. . . The claim that they want to protect their eastern border from Iran and others is all lies.”

Israel explains its security concerns by pointing to the Gaza Strip, on its southern border. Israel withdrew from Gaza in 2005. The militant Islamic organization Hamas came to power two years later. Now, rockets and shoulder-fired missiles are routinely smuggled into Gaza from Egypt, Israeli officials say. They note that no such weapons have been found in the tightly-controlled West Bank.

“The Israeli government is concerned that the Palestinian side will not be interested or not be able to carry out its part of the deal,” said Giora Eiland, a retired major general in the Israel army and former head of Israel’s National Security Council. “What happens if this deal is signed tomorrow, Israel withdraws and a day later Hamas takes over the West Bank?

“This is the Israeli concern, and this creates a lot of suspicions and agitation on the Israeli side,” he said.

Kerry and his team have tried to help Israel overcome its fear with offers of U.S.-provided intelligence and technology — but Israel already has sophisticated drones, surveillance technology and some of the best “smart fences” in the world.

At one point, U.S. diplomats discussed placing international troops in the Jordan Valley. But Israeli hawks pointed to failures by U.N. forces in demilitarized zones along the Lebanon and Syrian borders.

Another proposal calls for a combination of Palestinian and Israeli security forces at border crossings and a strip of territory along the Jordan River.

“The question now is, for how long will the Israelis be there?” Eiland said. “Will it mean a permanent Israeli presence or for a limited period of time? Does that mean two years, five years, 15 years or 50 years?”

Gearan reported from Washington. Ruth Eglash in Jerusalem contributed to this report.