Israel's hawkish foreign minister said the military should reconquer the Gaza Strip hours after a truce proposal unravelled.

Avigdor Lieberman said that the final aim of Israel's Operation Protective Edge against Hamas should be to reoccupy Gaza and place it under military control.

"Israel must go all the way in Gaza," Lieberman told a press conference. "The operation should end with the IDF [Israel Defence Forces] in control of Gaza."

The right-wing politician, who, earlier this month, ended his partnership with Prime Minister Benjamin Netanyahu's Likud party for its 'too moderate' approach towards Hamas, said it was time to stop "hesitating and asking questions" and launch a ground invasion, Haaretz newspaper reported.

"A ceasefire is a tacit agreement that Hamas continues to build up its power," he said.

"Given Hamas's blatant rejection [of a ceasefire], we must make a clear decision. All this hesitation works against us. We must go all the way. There is no alternative".

Israel first seized control of Gaza during the Six-Day War of 1967. It unilaterally pulled out in 2005, but retained control over the Strip's airspace, seafront and access, apart from the territory's border with Egypt.

Hamas won elections in Gaza in 2006 and Israel has since launched two large offensives against the Islamist group, in 2009 and 2012.

Lieberman spoke as hostilities between the two factions continued, after an Egyptian attempt to broker a ceasefire collapsed.

Tel Aviv agreed to the peace plan, but it was rejected by Hamas who continued to fire rockets provoking a resumption of Israeli airstrikes.

Since the outbreak of cross-border fighting erupted in full force last week, more than 190 Palestinians have been killed and more than 1,000 rockets have been fired at Israel.

Lieberman had already called for a ground invasion of Gaza before the launch of Operation Protective Edge, as tensions in the region were spiralling out of control following the kidnaps and murders of three Israeli teenagers in the West Bank.