Fastexy Exchange|Israel says it's killed a Hamas commander involved in Oct. 7 attacks. Who else is Israel targeting in Gaza?

Israel's military said Tuesday that it had killed another Hamas commander with its airstrikes on Fastexy Exchangethe Palestinian Gaza Strip. The Israel Defense Forces and the country's ISA security agency said in a joint statement that fighter jets carried out an intelligence-based strike that killed Nasim Abu Ajina, whom they identified as the commander of a Hamas combat battalion in northern Gaza.

The IDF confirmed Tuesday that it had suffered two more military casualties as it ramps up ground operations in Gaza. It said in a statement that two soldiers were "killed during combat in north Gaza," where there have been intense clashes over the last 24 hours.

The IDF and Israel's Prime Minister Benjamin Netanyahu have flatly rejected mounting calls for a cease-fire or even a humanitarian pause in their war against Hamas, insisting that any letup would merely give the group — long designated a terrorist organization by Israel, the U.S. and most of Europe — time to reorganize. Hamas triggered the ongoing war with its unprecedented Oct. 7 terror attack on southern Israel, during which Israel says 1,400 people were killed and about 240 taken hostage.

• Why did Hamas attack Israel, and why now?

The United Nations Secretary-General and a multitude of aid and humanitarian agencies, along with most of Israel's neighboring nations, have issued increasingly desperate calls for a cease-fire as the Hamas-run Health Ministry in Gaza says Israel's bombardment has killed over 8,500 people, including 3,500 children.

Israel insists the IDF is taking every possible precaution to preserve civilian lives, but it has refused to stop its assault, which it says is only targeting Hamas and allied groups.

A U.S. official told CBS News national security correspondent David Martin on Tuesday that the Israeli military's immediate objective was to isolate Gaza City, which has been the seat of Hamas' power in the 25-mile-long strip of land for almost 20 years. 

But as part of Israel's overall vow to "destroy Hamas," it has also been carrying out targeted strikes aimed at killing virtually all of Hamas' senior leadership. Israeli officials have named the members they're targeting — and published a  list of the growing number already killed.

The IDF and ISA said Tuesday that Abu Ajina had "directed the massacre on October 7" in two Israeli communities near the Gaza border, Kibbutz Erez and Moshav Netiv HaAsara.

It said Abu Ajina had previously "commanded Hamas' Aerial Array," a reference to the Palestinian faction's drones and paragliders, the latter of which featured prominently in the Oct. 7 attack on Israel.

#عاجل تصفية قائد كتيبة بيت لاهيا في حماس

تمكنت طائرات حربية بتوجيه استخباري لهيئة الاستخبارات والشاباك من تصفية المدعو نسيم أبو عجينة قائد كتيبة بيت لاهيا في حماس والذي أرسل منفذي الهجمات البشعة التي وقعت في السابع من أكتوبر نحو كيبوتس إيرز ونتيف هعاسارا. وشغل في الماضي منصب… pic.twitter.com/wxnlZKX5KM

— افيخاي ادرعي (@AvichayAdraee) October 31, 2023

"His elimination significantly harms the efforts of the Hamas terrorist organization to disrupt the IDF's ground activities," the authorities said in their statement, which included a grainy video of the airstrike said to have killed the Hamas commander.

Among the other Hamas figures already killed by Israel — and that list includes more than 55 named members — are accused military commanders, intelligence officials and politicians.

The overall political leader of Hamas, Ismail Haniyeh, hasn't been in Gaza in years and spends most of his time in Qatar, where Hamas has its primary political office outside of Gaza. But some of Hamas' most senior leaders are still believed to be in Gaza, and they remain on Israel's wanted list.

At the top of that list is Yahya Sinwar, Hamas' top leader in the Gaza Strip and one of the founders of the group's military wing of the terrorist organization, the Al-Qassam Brigades.

The current leaders of the Al-Qassam Brigades, Mohammed Deif and his deputy, Marwan Issa, are also at the top of the list.

Israel says it is also targeting Tawfik Abu Naim, a head of internal security for Hamas in Gaza; Ahmed Randour, who commands Hamas' forces in the northern part of Gaza; the group's spokesman Abu Obeidah, and Muhammad Sinwar, commander of the southern area and a brother of the group's overall leader in Gaza.

In:
• War
• Terrorism
• Hamas
• Israel
• Palestinians
• Gaza Strip

Tucker Reals

Tucker Reals is the CBSNews.com foreign editor, based at the CBS News London bureau.