Critics say the proposal by Mr Netanyahu's far-right government is an attack on the country's democracy because it would make it harder for the Supreme Court to rule against the legislature and the executive branches.
"We welcome this announcement as an opportunity to create additional time and space for compromise. A compromise is precisely what we have been calling for," White House spokeswoman Karine Jean-Pierre said.
"We continue to strongly urge Israeli leaders to find a compromise as soon as possible."
Mr Netanyahu on Monday delayed the decision on his plans for a judicial overhaul until next month amid fears that the country's worst national crisis in years could fracture his coalition or escalate into violence.
Mr Biden "definitely shared his concerns over this legislation with Prime Minister Netanyahu directly", White House National Security Council spokesman John Kirby said on Monday.
"It really does come from a place of supporting the very idea of checks and balances."
Amid the domestic and international backlash, Mr Netanyahu on Monday delayed his proposals to allow for greater public discussions.
Mr Kirby said the White House remained "deeply concerned" by recent developments, "which further underscored our view of the urgent need for compromise".
Israeli backlash grew over the weekend after Mr Netanyahu fired his defence minister, Yoav Gallant, who spoke out against the reform bill.
Aaron Miller, who was a Middle East adviser to the US State Department, said there was little the Biden administration could do from a practical standpoint to influence Israeli policy on the issue.
"On judicial reform, they basically made a decision to allow the Israelis to do the walking and the talking, and that's as it should be," Mr Miller told The National.
"Watch what's going on in the streets over the last 13 weeks, an extraordinary demonstration of coherence and resolve …
"The administration could not do any better than that. They will encourage from the sidelines, they'll talk about the need for compromise and consensus."
US Secretary of State Antony Blinken last week told Congress that the proposal was an "internal matter", but when Mr Biden spoke to Mr Netanyahu it was a "pretty tough" phone call, Mr Miller said.
"But there's not much they can do. I suspect they could only make matters worse if they start to intervene and intrude in Israeli politics," he said. "It's never worked out."
Mr Biden is this week hosting the second Summit of Democracy and Israel's presence there could have been awkward for the White House had Mr Netanyahu pressed ahead with his overhaul of the judiciary.
Jonathan Schanzer, senior vice president for research at the Foundation for Defence of Democracies, which studies Israel closely, said the Biden administration could have been left in a tough spot if the proposed reforms had passed.
"We'd likely have seen some tough words from the White House about the weakening of Israeli democracy," Mr Schanzer told The National from Tel Aviv.
"It certainly could have put Israel in a precarious situation where it would be seen as a less robust democracy or weaker than it had been the day before."
Bob Menendez, chairman of the Senate foreign relations committee, said he was closely watching developments in Israel.
"I urge all to continue to heed voices calling for calm and consensus building," Mr Menendez wrote on Twitter.