The military overthrow of deposed Egyptian president Mohammad Morsi was a blow to Hamas in Gaza, Army Radio cited Public Security Minister Yitzhak Aharonovitch (Likud Beytenu) as saying on Saturday.
Aharonovitch, speaking at a cultural event in Beersheba, added that Israel had maintained a good connection with the government of Egypt's first democratically elected president.
The minister attested to the importance of preserving relations with Egyptian armed forces following Morsi's ouster.
Palestinian Authority leaders on Thursday expressed joy over the downfall of Morsi’s regime, with some calling on Palestinians in the Gaza Strip to follow suit and topple the Hamas government.
Palestinian analysts predicted that the collapse of the Muslim Brotherhood regime in Egypt would undermine Hamas, which in the past year has been emboldened by Morsi’s rise to power.
PA President Mahmoud Abbas was one of the first Arab leaders to congratulate the Egyptians on the ouster of Morsi.
On Thursday, former IDF chief of staff Gabi Ashkenazi said Morsi's overthrow, and the Egyptian army's takeover of the country, did not pose any immediate danger to Israel.
"I think the Egyptian army is too busy [with domestic issues] to deal with anything that is outside of Egypt, so I don't think there's any danger at the moment," Ashkenazi said.
"Even in the year the Muslim Brotherhood was in power, they did not renege on the peace treaty [with Israel], and as far as stopping smuggling [from Sinai into the Gaza Strip] and handling Hamas, they were reasonable," he added.
Ashkenazi cautioned, however, that Israel needed to carefully observe the volatile situation in Egypt as the unfolding drama was still "far from over."
The Israeli government meanwhile took a cautious approach to the developments in Egypt.
A spokesman for Prime Minister Binyamin Netanyahu declined to comment on Morsi's removal by the Egyptian army, but a Netanyahu confidant, Tzachi Hanegbi, expressed hope the appointment of Adli Mansour would lead to the restoration of largely frozen contacts with Cairo.
Hanegbi, a member of Netanyahu's Likud party and of the Knesset's Foreign Affairs and Defense Committee, hailed what he described as continued good ties with Egypt's armed forces.
"There had been legitimate doubts [that a 1979 peace treaty with Egypt would hold] because in the past year Morsi, in a very harsh manner, broke off all diplomatic contacts with Israel," Hanegbi told Army Radio, describing the first peace treaty between an Arab country and Israel.
"Yesterday's events strengthen the feeling that perhaps we have passed the bad period and perhaps now there will be a chance to have diplomatic ties with whoever will govern Egypt in the near future," Hanegbi told Army Radio.
Gunmen shot dead a Coptic Christian priest in Egypt's lawless Northern Sinai on Saturday in what could be the first sectarian attack since the military overthrow of the former Islamist president, security sources said.
Overnight, at least 30 people died and more than 1,000 were wounded after Morsi's Muslim Brotherhood movement called "Friday of Rejection" protests across the country and tried to march on the military compound where the ousted president has been held.