The Palestinians rejected US proposals for Israel to keep a military presence in a future Palestinian state, as US Secretary of State John Kerry Friday wrapped up his latest peace push.

Kerry, on his way to Vietnam, made a stop in Jerusalem and the West Bank city of Ramallah in a bid to promote his security plans for a future Palestinian state in his second visit in less than a week.

On Thursday night he met Palestinian president Mahmud Abbas and on Friday Israeli Prime Minister Benjamin Netanyahu before leaving snow-hit Jerusalem for Ben Gurion airport in Tel Aviv, media reported.

"I'm delighted to be here. I'm on my way to Asia, heading to Vietnam and the Philippines, which is a long-promised trip," Kerry told reporters as he went into his talks with Netanyahu.

"But I wanted to come through here in an effort to try to continue our important discussions.

"It's been constructive. It's always complicated," he said.

"We have a lot to talk about, and we will continue this process."

Defence Minister Moshe Yaalon had also been due to attend the Kerry-Netanyahu talks, but his spokesman told AFP the weather prevented him from doing so.

After meeting Kerry in Ramallah, the Palestinian political capital, Abbas rejected US proposals for Israel to keep troops in a future Palestinian state along its strategic border with Jordan.

"President Abbas has rejected the ideas presented by the secretary of state," a Palestinian source said on Friday.

Palestinian red lines

Abbas also handed Kerry a letter laying down "Palestinian red lines", the source added, singling out "the refusal to recognise Israel as a Jewish state".

Abbas "rejected the ideas on security because there is not a third party".

This refers to a plan by former US national security adviser James Jones under which a third party would deploy along the Palestinian-Jordanian border.

The Palestinian source said that "all disputed issues must be settled".

Israeli and Arab media reports say the plan envisaged by Washington would see Israel maintain a military presence on the border after a peace agreement with the Palestinians.

According to pan-Arab daily Al-Quds al-Arabi, the plan also includes the deployment of early warning stations on the highest point in the West Bank, an Israeli right to deny entry to anyone through the Jordan Valley border crossing and joint Israeli-Palestinian patrols in the area.

An international force would be acceptable to the Palestinians, but Israel opposes such a solution.

Israel has always insisted that a continued military presence on the frontier would be vital for its security for some 10-15 years after Palestinian statehood.

Former Israeli national security adviser Giora Eiland wrote on Thursday in the Yediot Aharonot daily that Israel saw a potential threat as not coming necessarily from the Palestinians, but from "other enemies" in the region.

"Israel insists on having contiguous control along the Jordan River, and it seems like the Americans accept this," he wrote, saying Israel needed "a strip five kilometres (three miles) wide" to ensure its safety.

It was Kerry's ninth trip to Israel and the West Bank since March -- and his second in less than a week.

State Department spokeswoman Jen Psaki said this week the US was "focused on a final deal" rather than an interim agreement between Israel and the Palestinians.

Nine-month direct talks were launched between the sides by Kerry in July, and last week he said "we are closer than we have been in years" to reaching a deal.

But the Palestinians said Kerry's ideas on future security arrangements, which were presented to their leadership last week, had provoked a "real crisis".