It alleges Hamas, the Islamist movement that runs the Gaza Strip and with whom it has fought three wars since 2008, is seeking to use the protests as cover to carry out violence.
The protests are planned to last six weeks up until Nakhba Day, the anniversary of Israel's establishment that displaced hundreds of thousands of Palestinians.
The Israeli group B'Tselem, in a rare appeal, urged Israeli soldiers to refuse such orders.
A White House envoy urged Palestinians to stay away from the fence.
Lieberman seemed to suggest the journalist was using a drone when he was killed, but two people who said they were with him on Friday rejected it.
Last Friday, thousands of Gaza residents participated in the demonstration, many gathering in five tent encampments set up along the narrow coastal strip's border with Israel, several hundred metres from the fence.
Whereas 1000's of Palestinians have gathered for what are billed as nonviolent protests, dozens of younger males have approached the border and thrown stones, firebombs and burning tires towards the border fence.
More Palestinians were killed along the Gaza-Israeli border as demonstrators returned for the second consecutive Friday.
The Times of Israel is reporting that the IDF is claiming that the protesters who were killed or hurt by the IDF were all members of Hamas and committing acts of violence.
The IDF said it thwarted multiple efforts on Friday to breach the border fence - and that it used live fire to do so in some instances - as well as attempts to activate bombs against the troops under the cover of smoke from the protests.
Snapchat Introduces New Group Video Chat Feature
Snapcat is finally joining the rest of the messaging world with support for group video calling coming down the pipeline. The immitated becomes the immitator: It is now Snapchat's turn to co-opt hot features from less-popular rivals.
The crowd size was seen as a test for Hamas, an Islamic militant group that seized the territory in 2007 from its political rival, Palestinian President Mahmoud Abbas.
Speaking at U.N. headquarters in New York, Palestinian U.N. Ambassador Riyad Mansour put the death toll for Friday's protest at nine; the discrepancy between that figure and the death toll provided by the Gaza Health Ministry could not immediately be explained.
"They have a right to protest against their appalling conditions and the continuing blockade and occupation of Palestinian land, and in support of their right to return to their homes and their right to self-determination".
The blockade has made it increasingly hard for Hamas to govern.
Gaza's economy has been devastated by years of Israeli military attacks and a joint Israeli-Egyptian blockade.
Opposition leader Avi Gabbay also defended the IDF, which, he said, "showed determination, sound judgement and created deterrence in the face of Hamas's provocations".
Israel says it has no selection, accusing Hamas of attempting to smuggle weapons and supplies that may turn into weapons into the territory.
Israel says it is doing what it must to defend its border and that its troops have been responding with riot dispersal means and fire "in accordance with the rules of engagement".
"There are no innocent people in the Gaza Strip", Mr Lieberman told Israel's public radio.