The Israelis have told the U.S. that the current phase of their offensive against Hamas, with heavy air strikes and a large ground operation, should be complete in the next 2-3 weeks, according to two U.S. officials.

One official cautioned that this would not mean an end to combat operations, but it would bring about a reduced intensity and a lower level of bombing with more targeted strikes while the Israelis pursue the remaining leadership of Hamas. 

In a meeting with national security adviser Jake Sullivan Thursday, the Israeli defense minister said the war "will last more than several months," predicting the next phase of targeted raids is likely to be a long one.

The U.S. has been urging Israel to do more to protect civilians as it conducts its offensive. Earlier this week, President Biden warned that Israeli Prime Minister Benjamin Netanyahu's government was losing international support due to "indiscriminate bombing" in the densely populated region. And on Thursday, during a visit to the National Institutes of Health, the president was asked if he wants Israel to scale back its offensive.

"I want them to be focused on how to save civilian lives," he replied. "Not stop going after Hamas, but to be more careful." 

The Biden administration has been facing mounting criticism for its response to the war, including the U.S.' refusal to call for a new cease-fire. The White House and Netanyahu have argued that any new truce would allow Hamas militants to regroup.

Health officials in the Hamas-run Gaza Strip say more than 18,000 people have been killed during the conflict. Israeli Prime Minister Benjamin Netanyahu has shown no willingness to ease the bombing campaign in southern Gaza despite catastrophic losses of civilian life and uncertainty over the fate of more than 100 hostages who are still believed to be held in the territory. 

Israel's military says Hamas militants killed 1,200 and kidnapped over 200 in their Oct. 7 terror rampage across southern Israel. About half the hostages have been released, most of them during a week-long cease-fire.

Ed O'Keefe and Tucker Reals contributed to this report.

In:
• Hamas
• Israel
• Gaza Strip

David Martin is CBS News' National Security Correspondent.