A correspondent for US Cable News Network television, Ben Wedeman, was hit in the waist by a bullet in the Gaza Strip. His injuries were not life-threatening, CNN said.
An Israeli Government spokesman said Mr Peres, who shared a Nobel Peace Prize in 1994 with the Palestinian leader, was one of the few Israelis who could still talk to Mr Arafat. A meeting may be arranged later on Tuesday.
Mr Arafat, whose command centres in the West Bank and Gaza Strip were attacked by Israeli helicopter gunships on Monday night, said his people would not be cowed by the raids.
At least five Palestinians have been killed in clashes with Israeli soldiers on Tuesday.
A correspondent for US Cable News Network television, Ben Wedeman, was hit in the waist by a bullet in the Gaza Strip. His injuries were not life-threatening, CNN said.
The Palestinian leadership called for help from the United Nations, the Arab world and the European Union, as the Israeli helicopter raids signalled new and more aggressive tactics.
Barak under pressure
In the raids, targets were hit in the West Bank towns of Nablus and Ramallah, as was a building used by Mr Arafat's Force 17 militia in Khan Yunis, Gaza.
The Israeli Prime Minister, Ehud Barak, is struggling to keep his minority government in power. The leader of the opposition Likud party, Ariel Sharon, has vowed to topple him, making it less likely that Mr Barak will be able to form a national unity government.
In Gaza, officials at Shifa hospital said four Palestinians were shot dead in clashes at the Karni commercial crossing between Gaza and Israel.
Another Palestinian died after being shot in skirmishes at al-Jalazon refugee camp in the West Bank.
The latest deaths raise to more than 155 the number of people killed or declared clinically dead - the vast majority of them Arabs - in nearly five weeks of violence in the Palestinian territories.
The death of an Israeli man, whose bullet-riddled body was found in a Palestinian-controlled West Bank village at the weekend, raised to 11 the number of Israeli troops and Jewish civilians killed.
New Israeli tactics
The Israeli military says it is switching to pinpoint strikes on specific Palestinian targets and deploying special units trained in guerrilla warfare.
Mr Arafat said the helicopter raids "cannot shake one eyelash from the eyelashes of a Palestinian child holding a Palestinian stone to defend holy Jerusalem".
"Whoever dislikes it, let them come and drink the sea of Gaza," he said.
Mr Barak disclosed earlier that he had spoken with the Palestinian leader last week and "let him know our positions."
The phone call would have come just after the Israeli leader declared an indefinite "time-out" in the Middle East peace process.