The proposed independent Palestine alongside Israel would have no army of its own, only a police force, Assad told the New York Times. So the NATO forces would be in charge of ending weapons smuggling and quashing terrorism, major Israeli concerns, he said.
The NATO troops could stay in the West Bank "for a long time, and wherever they want, not only on the eastern borders, but also on the western borders, everywhere," Abbas said.
"The third party can stay. They can stay to reassure the Israelis, and to protect us," he said.
"We will be demilitarized. Do you think we have any illusion that we can have any security if the Israelis do not feel they have security?"
In an interview about the struggling Israeli-Palestinian peace talks, Abbas also said Israeli soldiers could remain in the West Bank for up to five years -- not the three years he earlier proposed -- and said he envisioned Israeli settlements being phased out of the new Palestinian state during those five years.
The office of Israeli Prime Minister Binyamin Netanyahu declined to respond directly to Abbas' NATO proposal.
"Our attitude toward international forces is skeptical in the extreme," a senior Israeli official told the newspaper.
Netanyahu has often said Israel would rely on its own military and no other.
Illustrating that point, Abbas told the Times he once suggested to Netanyahu a U.S.-led force including Jordan could patrol the West Bank.
The suggestion came a few years ago at Netanyahu's home in a meeting with then-Secretary of State Hillary Clinton, he said.
"I told him: 'If you will not trust your allies, so whom do you trust? I am not bringing for you Turkey and Indonesia,'" Abbas recalled saying to Netanyahu.
"He said, 'I trust my army only,'" Abbas said.
State Department spokeswoman Jen Psaki told the Times in an email, "There are many ideas being proposed from both the Israelis and the Palestinians, but it is premature to make any predictions about the final contents of a framework."
Kerry is preparing to present a framework of core principles for a peace deal. The framework is expected to include a security plan, an Israeli-Palestinian border roughly along the 1967 lines, Palestinian recognition of Israel as a Jewish state and Jerusalem as a shared capital.
The peace talks started July 29, 2013, and are scheduled to last up to nine months, or until April 29. Kerry originally said the talks would reach a final Palestinian-Israeli accord by that date but later proposed simply an agreement on a preliminary framework.
April 29 is "not a sacred date," Abbas told the Times.
"Suppose by the end of nine months we got something promising. Shall I stop? I will not stop," he said. "If, after nine months, we didn't get anything, if there is nothing on the horizon, we will stop."
Abbas also said recognition of Israel as a Jewish state was "out of the question."
He said Egypt and Jordan were not asked to do this when they signed peace treaties with Israel.
He showed the Times a 28-page packet that included a 1948 letter signed by President Harry Truman in which "Jewish state" was crossed out and replaced by "State of Israel."
The first U.S. official to use "Jewish State" was Secretary of State Colin Powell in a 2001.
For Netanyahu, Palestinian recognition of Israel as a Jewish state would mean Palestinian refugees have no claim to return to property they fled or were forced to leave when Israel was founded in 1948, the Washington Post said.
Palestinians see their "right of return" as a sacred tenet.
The Palestine Liberation Organization recognized Israel in 1993 as part of the Oslo Accords.