It circulated a one-page draft text, seen by Reuters, to the 15-member council. A resolution needs at least nine votes in favor and no vetoes by the U.S., France, Britain, China or Russia to pass.
The draft calls on Hamas to accept the deal and "fully and implement its terms without delay and without condition." It also "stresses the importance of the parties adhering to the terms of the deal once agreed, with the aim of bringing about a permanent cessation of hostilities."
The U.S. proposal comes a week after Algeria proposed a draft Security Council resolution demanding a Gaza ceasefire, release of all hostages held by Hamas and essentially ordering Israel to "immediately halt its military offensive" in Rafah.
Biden on Friday laid out what he described as a three-phase Israeli proposal for a ceasefire in Gaza in return for the release of Israeli hostages, saying "it’s time for this war to end".
The new proposal would begin with a six-week ceasefire in which the Israel Defense Forces (IDF) would withdraw from populated areas of Gaza.
There would also be a "surge" of humanitarian aid, as well as an exchange of some hostages for Palestinian prisoners.
The deal would eventually lead to a permanent "cessation of hostilities" and a major reconstruction plan for Gaza.
Hamas said it views the proposal "positively".
Speaking at the White House on Friday, Mr Biden said that the first phase of the proposed plan would include a "full and complete ceasefire", the withdrawal of IDF forces from populated areas and the exchange of hostages for Palestinian prisoners.
"This is truly a decisive moment," he said. "Hamas says it wants a ceasefire. This deal is an opportunity to prove whether they really mean it."
The ceasefire, he added, would allow more humanitarian aid to reach the beleaguered territory, with "600 trucks carrying aid into Gaza every single day".
The second phase would see all remaining living hostages returned, including male soldiers. The ceasefire would then become "the cessation of hostilities, permanently."
The third phase of the proposal would see the final remains of any deceased Israeli hostages returned, as well as a "major reconstruction plan" with US and international assistance to rebuild homes, schools and hospitals.
