Mohammed Abu Shamala, Mohammed Barhoum and Raed al-Attar died in the attack near the southern town of Rafah.
They were among at least six killed, a day after Hamas’s military chief Mohammed Deif reportedly survived a strike that killed his wife and child.
An Israeli was severely injured as rockets were fired into Israel on Thursday, the army said.
Hostilities resumed after peace talks collapsed on Tuesday.
Israel has vowed to pursue its campaign until “full security” is achieved.
Six weeks of fierce fighting have left at least 2,103 people dead, all but 67 of them Palestinians and most of them said to be civilians.
Israel’s strike on Rafah demolished a four-storey building and “dozens” of people were missing, Palestinian health official Ashraf Al-Kidra was quoted as saying by AP news agency.
The three commanders killed were key to operations including smuggling, tunnel construction and capturing the Israeli soldier Gilad Shalit in 2006.
Israel’s military said it had carried out 20 attacks on targets in Gaza during the night in response to militant rocket attacks. Since talks on extending the ceasefire failed, 213 rockets have been fired at Israel, it added.
According to an unconfirmed report by AFP news agency, at least six other Palestinians, four of them children, were killed in Israeli attacks overnight in the northern town of Beit Lahiya and in Gaza City.
In another development, Hamas warned foreign airline companies to stop flying to and from Tel Aviv’s Ben Gurion Airport from Thursday.
Ofer Lefler, spokesman for the Israel Airports Authority (IAA), told AFP that flights had been disrupted for 10 minutes but there had been “no change to take-offs or landings”.
Hamas also confirmed it was abandoning efforts to negotiate a durable ceasefire with Israel.
It had gone to the talks in Cairo demanding an end to the Israeli and Egyptian blockades of Gaza, and the establishment of a seaport and airport.
Israel, for its part, had sought guarantees that Hamas and other factions in Gaza would be disarmed,
The UN Security Council voiced “grave concern” at the resumption of hostilities and “called upon the parties to resume negotiations to urgently reach a sustainable and lasting ceasefire”.
Egypt expressed “profound regret” at the end of a 10-day period of “calm” during the talks, and said it would continue to try to secure a lasting truce.
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