Secretary of State John Kerry makes a statement to the press before a meeting at the Prime Minister's Office in Jerusalem, Jan. 2, 2014. (Brendan Smialowski/AFP/Getty Images)

Speaking to a private audience about the Middle East peace process, Secretary of State John Kerry did what for many Israel supporters is the unthinkable and used the A-word: apartheid.

"A two-state solution will be clearly underscored as the only real alternative. Because a unitary state winds up either being an apartheid state with second-class citizens - or it ends up being a state that destroys the capacity of Israel to be a Jewish state," Kerry said Friday in remarks originally reported by the Daily Beast.

For many Jewish groups, the suggestion that Israel is, or even could be, carrying out the systematic oppression and discrimination of Palestinians living within its borders is anathema - despite the fact that major Israeli officials, including Justice Minister Tzipi Livni and former Prime Minister Ehud Barak, have acknowledged the risk that it could become an apartheid state.

Kerry's comments also come at a particularly sensitive time in the Middle East, as the deadline for the current round of nine-month peace talks is Tuesday, with no sign that negotiations will be extended.

State Department spokeswoman Jen Psaki sought to put Kerry's comments in context Monday, noting that he remains committed to a two-state solution and was not accusing Israel of having a current policy of apartheid.

"The secretary does not believe and did not state publicly or privately that Israel is an apartheid state, and there's an important difference there. Israel is obviously a vibrant democracy with equal rights for all of its citizens," she said.

"He certainly didn't say 'is,'" she added later.

The American Israel Public Affairs Committee, or AIPAC, countered that it is never acceptable to link Israel with the practice of apartheid.

"Any suggestion that Israel is, or is at risk of becoming, an apartheid state is offensive and inappropriate," AIPAC's statement read in part. "Israel is the lone stable democracy in the Middle East, and protects the rights of minorities regardless of ethnicity or religion."

And it didn't take long for members of Congress to weigh in, with House Majority Leader Eric Cantor, R-Va., releasing a statement urging Kerry to apologize to the Israeli government and people.

"The use of the word apartheid has routinely been dismissed as both offensive and inaccurate, and Secretary Kerry's use of it makes peace even harder to achieve," the statement read in part.

Sen. Ted Cruz, R-Texas, suggested Kerry shouldn't even have the chance to apologize, as he took to the Senate floor to call for the secretary to step down.

"Before any further harm is done to our alliance with Israel, he should offer President Obama his resignation and the President should accept it," Cruz said.