Israel and Hamas are pushing forward with tense cease-fire talks despite Israel's military incursion into Rafah

• Israel and Hamas are engaged in tense cease-fire talks despite fighting in Rafah.
• Israel's prime minister rejected the latest proposal, saying it fell "very far" from its demands.

Cease-fire talks to end the fighting in Gaza are still taking place in the background, despite Israel's military incursion into Rafah.

Negotiators from both Israel and Hamas are in Cairo, having arrived hours after Israeli tanks and troops entered the city of Rafah, according to The New York Times.

The Israel Defense Forces said Tuesday it had taken operational control of the Gazan side of the Rafah border crossing after carrying out what it described as "targeted" strikes against Hamas in the city's eastern sector.

In a military update on Tuesday, the IDF international spokesperson Nadav Shoshani said it had urged local residents to "temporarily" evacuate the eastern part of Rafah to a humanitarian area ahead of what he called a "counterterrorism" operation.

Shoshani said that IDF troops eliminated 20 Hamas militants in the first hours of the operations, adding that humanitarian aid would continue to flow inside Gaza.

The IDF's military operation comes as Israel and Hamas are engaged in tense talks to broker a cease-fire.

On Monday, Hamas said it had accepted a deal proposed by Egypt and Qatar.

It would guarantee the release of all Israeli captives in Gaza — civilians or military, whether they're alive or not — from any time in exchange for a number of prisoners held by Israel, per a copy of the proposal obtained by Al Jazeera.

The proposal also called for the return to a "sustainable calm" that would lead to a permanent cease-fire and a withdrawal of Israeli forces from the Gaza Strip, its reconstruction, and the end of the siege, per the outlet.

But in a statement Tuesday, Prime Minister Benjamin Netanyahu rejected the proposal, saying it was designed to "torpedo" the entry of IDF forces into Rafah and fell "very far" from Israel's core demands.

Israel's government press office didn't immediately respond to a request for comment from Business Insider.

Ismail Haniyeh, the leader of Hamas' political wing, accused Netanyahu of "sabotaging the efforts made through the mediators," per Sky News.

Since Israel started its military operation in Gaza following Hamas' terror attacks on October 7, an estimated 2.3 million Palestinians have been driven out of their homes, and more than 34,500 civilians killed, AP reported Saturday, citing local health officials.

Over 1,100 people were killed in Hamas' attacks, and hundreds were captured. Many are still missing.

Mairav Zonszein, a senior analyst on Israeli domestic politics at the International Crisis Group, said Israel wanted to retain the authority to carry out further operations in Gaza.

"If you enter a cease-fire deal, then you will [eventually] need a cease-fire," she told Al Jazeera.

Yossi Mekelberg, an associate fellow at Chatham House's Middle East and North Africa Program, made a similar statement, saying the Israeli government was biding its time to continue military operations in Gaza.