Live updates: Follow the latest on Israel-Gaza
Mr Biden said his administration was in contact with the Israelis on the issue.
“My hope and expectation is that there will be less intrusive action relative to hospitals and we remain in contact with the Israelis,” Mr Biden told journalists at the White House.
“Hospitals must be protected.”
Mr Biden's comment came as Israeli forces have been engaging in gun battles and launching air strikes around Al Shifa Hospital, Gaza's largest and most advanced medical facility.
Palestinian health officials said patients and people taking refuge in the hospital became trapped as Israeli tanks circled the compound.
They also said as many as 200 bodies were decomposing outside an emergency ward of the hospital, with workers have been unable to bury them due to Israeli snipers.
White House National Security Adviser Jake Sullivan said although Israel has a right “to go after Hamas”, it must do so according to the laws of war.
“We do not want to see firefights in hospitals,” Mr Sullivan said during a news briefing. He added that it could put innocent people who are seeking medical care in the crossfire.
The calls come amid rising pressure on the Biden administration over the worsening humanitarian crisis and the rising death toll of Palestinians in Gaza, which has exceeded 11,100 people, the majority of them women and children, according to Gaza officials.
Israel says it wants to eradicate Hamas after the group attacked on October 7, killing about 1,200 people and taking about 240 hostage.
Israeli forces have been bombarding the coastal enclave with air strikes and have launched a massive ground invasion.