"On the war between Israel and Hamas, we're on the brink of a proposal that I laid out in detail months ago finally coming to fruition," Biden said during an address at the State Department, adding that he had learned during his long career in public service "to never, never, never, ever give up."
"The Palestinian people deserve peace and the right to determine their own futures. Israel deserves peace and real security. And the hostages and their families deserve to be reunited," the president continued. "And so, we're working urgently to close this deal."
In advance of the president's speech, confidence that the ongoing high-level talks could finally yield a long-awaited ceasefire agreement bloomed across Washington as the White House signaled a deal could be cemented before the Biden leaves office within a week.
"We are close to a deal, and it can get done this week," national security adviser Jake Sullivan said during a press briefing at the White House. "I'm not making a promise or a prediction, but it is there for the taking and we are going to work to make it happen."
Other members of the administration were even more cautiously optimistic, predicting that the next 24 hours would likely be "make or break" for the negotiations.
The current proposal on the table calls for an initial ceasefire period lasting at least six weeks in exchange for the release of around 30 living or dead hostages held in Gaza, according to officials familiar with the talks, who add that Israel is also expected to release more than a thousand Palestinian prisoners and detainees.
The officials say many of the specifics, including the exact number of hostages that would be turned over, are still being worked out, but that Hamas has indicated it is willing to hand over at least two of the seven American citizens the group is holding -- Sagui Dekel-Chen, 36, and Keith Siegel, 65.
While the Biden administration has been pushing Israel and Hamas to sign onto a version of the current deal since the president outlined his framework for three-stage peace pact in late May, members of the incoming Trump administration have played an increasingly significant role in the mediation process as the inauguration draws closer.
Sullivan said that coordination served to present "a united message" that it is "in the American national security interest, regardless of party, regardless of outgoing or incoming administration to get this deal done as fast as possible."
The Trump team's involvement is also necessary from a practical standpoint since the U.S. would act as a guarantor of any deal that comes to fruition and the Biden administration won't be in power long enough for it to play out.
President-elect Donald Trump has warned Hamas repeatedly that "all hell will break out in the Middle East" if the hostages aren't released by his taking office on Jan. 20.
Ahead of his speech at the State Department, Biden said he had worked the phones -- speaking with the leader of Qatar, a critical intermediary with direct lines to Hamas, on Monday and talking with Israeli Prime Minister Benjamin Netanyahu on Sunday, according to the White House.
Biden said he would also soon speak to Egypt's President Sisi, another key broker overseeing the negotiations.
Ukraine, Iran
The president also focused part of his remarks on Russia's war in Ukraine, touting the administration's efforts to bolster Ukraine and global alliances in the process -- noting that 23 NATO countries are now spending 2% of the GDP on defense, up from nine when he took office.
"Today, I can report to the American people our adversaries are weaker than where we came into this job four years ago. Just consider Russia. When Putin invaded Ukraine, he tried to conquer Kyiv in a matter of days. But the truth is, since that war began, I'm the only one who stood in the center of Kyiv, not him. Putin never has. Think about it," he said.
"We help Ukrainians stop Putin. And now, nearly three years later, Putin has failed to achieve any of his strategic objectives," Biden said.
"Today, Ukraine is still free, independent country with the potential -- potential for a bright future. And we laid the foundation for the next administration so they can protect the bright future of the Ukrainian people," he later added
Biden touted the U.S. work help diminish Iran during his time in office as well, though noted he could not claim all the credit.
"Now, I cannot claim credit for every factor that led to Iran and Russia growing weaker in the past four years. They did plenty of damage all by themselves, but Israel did plenty of damage to Iran and its proxies. But there's no question our actions contributed significantly," Biden said.
Afghanistan
The president also addressed a low point of his administration, defending his decision to withdraw American troops from Afghanistan in 2021, an operation that killed 13 service members.
"In my view, it was time to end the war and bring our troops home and we did. I commend the courage of all those who served in Afghanistan. We grieve all 2,461 Americans made the ultimate sacrifice in the longest war in American history, and I grieve for those brave service members whose lives were lost during the withdrawal," Biden said. "We also thank those inside and outside of government, have done so much to help thousands of Afghan families resettle in the United States."
The president looked ahead in his speech as well, urging the incoming Trump administration to continue working on two major challenges for the future: artificial intelligence and the clean energy transition.
"I know, and some incoming administration -- some in the incoming administration are skeptical about the need for clean energy. They don't even believe climate change is real. I think they come from a different century. They're wrong. They are dead wrong. It's the single greatest existential central threat to humanity," Biden said in his strongest criticism of the incoming Trump team of the remarks.
ABC News contributed to this report.