"Israel is on a trajectory potentially to inherit an insurgency with many armed Hamas fighters left or if it leaves a vacuum filled by chaos, filled by anarchy and probably refilled by Hamas," Blinken said on NBC's Meet the Press.
Hamas fighters, he said, are returning to northern Gaza areas that Israel claimed to have cleared, and an assault on Rafah "risks doing terrible harm to civilians" without ending the Hamas presence there.
Israel's planned invasion of Rafah has helped fuel the deepest tensions in relations between Israel and its main ally in generations.
U.S. National Security Adviser Jake Sullivan raised President Joe Biden's "longstanding concerns" over a major Israeli assault on Rafah in a call on Sunday with his Israeli counterpart, Tzachi Hanegbi, a White House statement said.
Sullivan discussed alternative courses of action to ensure the defeat of Hamas everywhere in Gaza, and Hanegbi confirmed Israel is taking U.S. concerns into account, it said without elaborating.
NBC and CBS News aired interviews with Blinken dominated by Biden's decision to pause a shipment of bombs to Israel over fears of massive civilian casualties in Rafah and a State Department report that Israel's use of U.S.-supplied arms may have broken international law.
The report, which was unrelated to the bomb shipment, found no specific violations justifying withholding U.S. military aid, saying the chaos of war prevented verification of alleged individual breaches.
Hamas' use of civilian infrastructure and tunnels "makes it very difficult to determine, particularly in the midst of war," what happened in specific instances, Blinken said, defending the report criticized by some lawmakers of Biden's Democratic Party and human rights groups.
Appearing after Blinken on NBC, Democratic Senator Bernie Sanders rejected the report, saying "any observer knows Israel has broken international law" and "should not be receiving another nickel in U.S. military aid."
Republican Senator Lindsey Graham, interviewed on the same program, called Biden's postponing the bombs "the worst decision in the history of the U.S. Israeli relationship."
"Give Israel the bombs they need to end the war they can't afford to lose, and work with them to minimize casualties," he said.
Defending the pause on the supply of 3,500 2,000-pound and 500-pound bombs, Blinken said Israel lacked a "credible plan" to protect some 1.4 million civilians sheltering in Rafah.
He told CBS the shipment was the only U.S. weapons package being withheld.
But that could change, he said, if Israel launches a full-scale attack on Rafah, which Israel says it plans to invade to root out entrenched Hamas fighters.
If Israel "launches this major military operation to Rafah, then there are certain systems that we're not going to be supporting and supplying for that operation," said Blinken.
Israel needs to "have a clear, credible plan to protect civilians, which we haven't seen," he said.
Most of the 1.4 million Palestinians in Rafah were displaced from elsewhere by fighting and Israeli bombardments that have devastated the seaside enclave.
Israel also has not developed a post-war plan for Gaza's security, governance and reconstruction, Blinken said, adding on CBS the U.S. is working on such a plan with Arab governments and others.
"We have the same objectives as Israel. We want to make sure that Hamas cannot govern Gaza again," he said, adding the United States has been discussing with Israel "a more effective, durable way" of demilitarizing Gaza and finding Hamas' leaders.
Israel's military operation in Gaza has killed at least 35,000 Palestinians, according to Gaza's Hamas-run health ministry.
The war was triggered by the Oct. 7 Hamas-led attack on Israel in which some 1,200 people were killed and more than 250 people taken hostage, according to Israeli tallies.
Israel says 620 soldiers have been killed.
