Up to 120 Palestinian protesters have been killed by Israeli fire since the rallies known as the "Great March of Return" started on March 30.
Israel announced plans to deduct from tax funds it collects for the Palestinians to compensate Israelis living near the Gaza Strip who have fallen victim to a wave of arson attacks.
"IDF troops thwarted an attempted infiltration from the Gaza Strip into Israeli territory by two terrorists who damaged the security fence and were armed with an ax", the army said in a statement.
Emphasizing that the Israeli violations against journalists increased in May, it added: "Nine of the journalists were hit by live ammunition, eight with explosive bullet shrapnel, 17 with gas bombs directly fired towards them, while 21 others barely escaped suffocating and fainted". It also urged the United Nations and other worldwide organizations to "investigate Israeli crimes and to prosecute those responsible and hold them accountable for their crimes".
There was no immediate comment from Palestinian officials on the incident, which comes at a time of renewed violence along the Israel-Gaza frontier.More news: Watch, stream as Justify gets post for Triple Crown bid
Since nonviolent protests began at the end of March, Israeli soldiers have killed at least 119 people, including 14 children.
Protests peaked on May 14 when at least 61 people were killed as tens of thousands approached the heavily fortified border in a demonstration coinciding with the controversial opening of the USA embassy in Jerusalem.
Al-Aqsa TV, affiliated with Gaza's ruling party, Hamas, published a video allegedly filmed on Monday showing a group of young men east of Khan Younis in the southern Gaza Strip, some of them using wire cutters to breach the fence.
No Israelis have been killed. "It's a shameful side that the United States made a decision to take".
More than 2 million Palestinians are packed into the narrow coastal enclave.