The fire balloons and air strikes are the latest violence heaping pressure on a fragile ceasefire between Israel and Gaza's Hamas rulers that came into place on May 21, ending 11 days of heavy fighting.

"Over the past day, arson balloons were launched from the Gaza Strip into Israeli territory," Israel's military said in a statement.

"In response... fighter jets struck military compounds and a rocket launch site belonging to the Hamas terror organisation."

AFP journalists in the Palestinian enclave also reported hearing explosions, which the army said hit sites in Gaza City and in Khan Yunis, in the south of Gaza, home to around two million people.

Soon after the strikes, Hamas militants opened fire with heavy machines guns towards the Jewish state, as Israeli warning air raid sirens rang out.

Palestinian militants in Gaza launched balloons for a third day running on Thursday, according to Israeli firefighters battling the blazes sparked by the devices.

The balloons are basic devices intended to set fire to farmland and bush surrounding Gaza.

After the first wave of fire balloons sparked blazes on Tuesday, Israel's military launched a retaliatory wave of strikes early Wednesday.

Then, as the balloons continued, the air force launched a second round of strikes overnight Thursday to Friday.

- Army ordered to increase 'readiness' -

This week's air strikes on Gaza were the first under Israel's new government headed by Naftali Bennett, whose ideologically disparate coalition on Sunday ousted long-serving prime minister Benjamin Netanyahu.

Israel army chief Aviv Kohavi late Thursday issued orders to "increase the IDF's (Israeli Defense Forces') readiness and preparedness for a variety of scenarios including a resumption of hostilities," the army statement read.

"The IDF will continue to strike military capabilities and infrastructure belonging to the terror organisation, and holds the Hamas as responsible for all events transpiring in the Gaza Strip," the statement added.

US Secretary of State Antony Blinken said he had spoken with Israel's new Foreign Minister Yair Lapid to offer support.

"We discussed America's unwavering commitment to Israel's security, our bilateral relationship, and the challenges ahead," Blinken tweeted after the Israeli strikes.

They also discussed "the need to improve Israeli-Palestinian relations in practical ways," State Department spokesman Ned Price said in a separate statement but there was no mention of the air strikes.

The new exchanges of fire come as Egypt tries to consolidate the ceasefire it helped broker.

The conflict killed 260 Palestinians including some fighters, according to Gaza authorities.

In Israel, 13 people were killed, including a soldier, by rockets fired from Gaza, the police and army said.

Cairo, along with the United Nations, is hoping to support the reconstruction of Gaza following a war that saw whole tower blocks reduced to smoking rubble and key infrastructure smashed.

The densely crowded Mediterranean enclave has been under an Israeli blockade since 2007.

Israeli army chief Kohavi is due to leave Tel Aviv on Saturday for a six-day visit to the United States for talks.

He is the first top Israeli official to do so since the new coalition government headed by Bennett took over on Sunday.

Kohavi will visit the US military's Central Command (Centcom) in Florida, with items on the agenda to include Gaza's Islamist rulers Hamas and Israel's arch-foe Iran, as well as Hezbollah, the Tehran-backed Lebanese Shiite Muslim group.

Kohavi will discuss "common security challenges", an army statement said, including issues "related to the Iranian nuclear threat, Iranian regional entrenchment in the Middle East, (and) Hezbollah's force build-up efforts".