The two nations agreed to an unconditional cease-fire following 11 days of fighting that led to intense international scrutiny and criticism of the response by Israel.
Critics – both foreign and domestic – have questioned President Biden on his stance after he reiterated his full support of Israel, but Blinken insists the administration wants to ensure an equal peace between Israel and the Palestinians.
"It's vitally important that the Palestinians feel hope and have opportunity and can live in security just as it is for Israelis," Blinken told "This Week" host George Stephanopoulos. "And there should be equal measures."
"The president has been very clear that he remains committed to a two-state solution," Blinken added. "Ultimately, it is the only way to ensure Israel's future as a Jewish and democratic state and of course, the only way to give the Palestinians the state to which they're entitled."
Blinken said a big part of that process would be to ensure that the Palestinian people feel "equal measures of security, of peace and of dignity."
However, progressive members of the Democratic Party have stood in stark opposition to any support of Israel: Sen. Bernie Sanders, I-Vt., introduced a resolution Thursday to force a vote on whether to block weapons sales to Israel.
House Democrats including Reps. Alexandria Ocasio-Cortez, D-N.Y., Mark Pocan, D-Wis., and Rashida Tlaib, D-Mich., filed a similar resolution on Wednesday.
Blinken instead praised the president’s response and "relentless focus on … quiet but effective diplomacy" to secure a cease-fire.
"If you go back and look at previous crises, they've lasted a lot longer," Blinken said. "But, of course, every single day that these things go on, we see a tremendous loss in human life and in human suffering. And we were determined to get to bring that to an end."
He also said Biden would consult Congress on "any" arms sale, though, the administration remains committed to "giving Israel the means to defend itself."
Fox News' Marisa Schultz contributed to this report.