'Biggest barrier' to Saudi-Israeli normalization is the two-state solution, says ex-CIA director

A two-state solution to the Israel-Palestinian conflict is "elusive" right now, according to former CIA director David Petraeus, adding that it is also the "single biggest barrier" to normalizing relations between Israel and Saudi Arabia.

"A solid path, a solid commitment to a two-state solution from Israel" is the biggest hurdle to Israel and Saudi's normalization plans, Petraeus, who is now chairman at KKR Global Institute, told CNBC's Dan Murphy.

Saudi Arabia does not recognize Israel as a state and has refused to do so since the Jewish nation's independence in 1948. However, there have been discrete but growing cooperation between them in recent years, raising hopes for a normalization agreement.

Achieving a diplomatic deal between two of America's most important allies in the Middle East was one of U.S. President Joe Biden's top foreign policy priorities.

But Oct. 7 changed everything. Palestinian militant group Hamas infiltrated Israel, killing more than 1,200 people and kidnapping dozens more.

In response, Israel waged a massive military offensive on the Gaza Strip which Hamas has controlled since 2007. More than 35,000 people have been killed in the Palestinian enclave so far, according to the health ministry there which is run by Hamas.

Saudi Arabia's official position is that it will not open diplomatic relations with Israel unless an independent Palestinian state is recognized.

"The Kingdom has communicated its firm position to the U.S. administration that there will be no diplomatic relations with Israel unless an independent Palestinian state is recognized," Saudi Arabia's Ministry of Foreign Affairs has said. 

The United Nations classifies Israel as an occupier state over the Palestinian territories, whose occupations and annexations following the 1967 Six-Day War remain in violation of international law.

While the two-state solution would bring about a "significant effect" in the region, Petraeus said it's not "all that realistic" right now.

The two-state solution refers to a broad concept of establishing two independent states: one for the Israelis and one for the Palestinians, in a bid to bring peace between the two sides.

Speaking to CNBC on Wednesday, Israeli Prime Minister Benjamin Netanyahu voiced opposition to the two-state solution, which was first touted by the Oslo Accords and is backed by many international actors.

"The two-state solution that people talk about basically would be the greatest reward for the terrorists," he told Sara Eisen.

Netanyahu stressed that the Gaza Strip would "immediately be taken over by Hamas and Iran," and instead, he championed an outcome in which Israel retains the "responsibility of overall security" over the Gaza enclave. 

Petraeus acknowledged that the U.S. has repeatedly tried to get out of the Middle East — as seen in its efforts to draw down in Afghanistan, but it keeps getting "sucked back."

"This region is far too important to the world, to the global economy," he said.

"When something bad happens in the Middle East, it tends to spew violence, extremism, instability, and in some cases, a tsunami of refugees, not just into neighboring countries in the region, but all the way into the countries of our most important NATO allies."

Two of Islam's holiest sites, Mecca and Medina, are also in Saudi Arabia, giving it a crucial role in the Muslim world when it comes to the issue of Palestine's statehood.

Saudi Arabia's Crown Prince Mohammed bin Salman once cited in an interview that a major sticking point toward this normalization was the Israeli-Palestinian conflict.

– CNBC's Joanna Tan, Ruxandra Iordache and Natasha Turak contributed to this report.