Israel-Gaza updates: 300,000 have fled Rafah, UN agency says

In his first comments since Israel's offensive into Rafah began, Prime Minister Benjamin Netanyahu said that Hamas' cease-fire proposal on Monday was "intended to torpedo the entry of our forces into Rafah."

"It did not happen. As the War Cabinet unanimously determined, the Hamas proposal is very far from Israel's necessary requirements," Netanyahu said.

"I instructed the working-level delegation that went to Cairo: continue to stand firm on the conditions necessary for the release of our abductees, continue to stand firm on the essential requirements for guaranteeing Israel's security," Netanyahu said.

-ABC News' Will Gretsky

Israeli tanks controlled Gaza's Rafah border crossing early Tuesday, as military officials accused Hamas of using the crossing for "terrorist purposes."

"Following intelligence that indicated that the Rafah Crossing in eastern Rafah was being used for terrorist purposes, IDF troops managed to establish operational control of the Gazan side of the crossing," Israel Defense Forces officials said in a statement.

Mortars had on Sunday been fired "from the area," killing four IDF soldiers, the Israeli military said.

A video and photos taken by the Israeli military and released Tuesday appeared to show several Israeli tanks operating on the Gazan side of the border.

-ABC News' Kevin Shalvey

The Israeli military moved into eastern Rafah late Monday to begin a "precise counterterrorism operation" targeting Hamas, the Israel Defense Forces said Tuesday.

IDF troops also took "operational control" of the Gazan side of the border crossing between Gaza and Egypt, officials said in a statement.

The operation in Rafah overnight included air strikes and on-the-ground troops, the military said. About 20 "terrorists" were killed and three tunnels were located, IDF officials said.

"IDF ground troops are continuing to operate against Hamas terrorist operatives and infrastructure in the area of the Rafah Crossing in eastern Rafah," the statement said.

-ABC News' Jordana Miller, Jessica Gorman and Kevin Shalvey

Qatar will send a delegation of mediators to Cairo on Tuesday to work on negotiations for a cease-fire deal, according to a spokesperson for the Qatari Foreign Ministry.

In a statement, the Qatari Foreign Ministry said they hope "talks will culminate in reaching an agreement for an immediate and permanent ceasefire in the Gaza Strip and the exchange of prisoners and detainees, and the sustainable flow of humanitarian aid into all areas of the Strip."