Hostage families plan to establish a "permanent encampment" outside of Israeli Prime Minister Benjamin Netanyahu's residence in Jerusalem, the Hostages and Missing Families Forum Headquarters said in a release Tuesday.

The families thanked President Donald Trump for his "ongoing support," but asked him to urge Netanyahu to make a deal and end the war.

"Our Prime Minister Netanyahu is not listening to our cries to save the hostages and end this war -- but he will listen to you! Bring him to the table for a deal that will bring everyone home!" the families said in a joint statement.

Protests outside Netanyahu's residence have begun.

-ABC News' Jordana Miller

It will likely take "a few months" for Israeli forces to complete their mission in Gaza City, according to the Israel Defense Forces (IDF).

"We estimate it will take a few months to take control of Gaza City and a few more months -- even more than that -- to clear the city of the infrastructure," IDF spokesperson Effie Defrin said in Hebrew during a briefing on Tuesday.

Overnight Tuesday, Israeli forces launched an intensified ground offensive in Gaza City. Before the operation began, about 300,000 people fled the city to head to southern Gaza, the IDF said Monday.

"Air, ground and intelligence forces" are working together to target Hamas military targets in Gaza City, Defrin said.

The Palestinian Authority called for "exceptional international intervention," to stop the IDF military campaign in Gaza City and across the Gaza Strip in a Tuesday statement from their Ministry of Foreign Affairs.

"It considers this an attempt to target civilians and transform Gaza City into a mass grave and an uninhabitable land, as is the case with the wider Gaza Strip. It also forces nearly one million Palestinians to flee and move amidst a vicious cycle of death," the Ministry of Foreign Affairs said in the statement.

-ABC News' Jordana Miller and Tom Soufi Burridge

President Donald Trump on Tuesday was asked by a reporter for his reaction to Israel beginning a ground offensive in Gaza City.

"We're going to see what happens because I hear Hamas is trying to use the old human shield deal, and if they do that, they're going to be in big trouble," Trump said as he left the White House ahead of a trip to the United Kingdom. "They're going to be in big trouble. They put it out two days ago that they're going to use the hostages as human shields."

The Chief of the General Staff of the Israel Defense Forces, Lt. Gen. Eyal Zamir, said Tuesday that expanding the ground operation in Gaza City "is a move of decisive importance for the continuation of the war."

"Yesterday we expanded the ground operation into the center of Gaza City, which constitutes a vital area for Hamas," Zamir told ground troops, as quoted in an IDF readout.

"The mission rests on your shoulders: to decisively defeat the Gaza City brigade," Zamir said, referring to the local Hamas unit.

The maneuver in Gaza City is a significant step to carry out our highest moral and important duty -- to return all the hostages home and to dismantle the military and governing capabilities of the Hamas terrorist organization," he added.

"The threat has changed, but so have we; we come better prepared," Zamir said.

-ABC News' Morgan Winsor