The Palestinians accuse Israel of escalating violence
The UN special envoy to the Middle East, Terje Roed-Larsen, criticised the killings as "unhelpful", and called for restraint from Israel.
He welcomed the action taken by Palestinian leader Yasser Arafat against militants, but warned that it must be deepened and broadened.
The other two Palestinians shot dead were killed in the West Bank. One was a member of the Islamic movement Hamas, whose militants have already rejected Mr Arafat's appeal as unworkable, the other was a naval policeman.
Israeli Prime Minister Ariel Sharon, who last week dismissed Mr Arafat as "irrelevant", made clear his disregard for the Palestinian leader's televised address.
"I thought it was unnecessary for me to see it," he said. "When it comes to the security of Israel, we relate only to deeds, not words."
Correspondents say the latest killings can only further complicate any attempts by Mr Arafat to rein in the militants vehemently opposed to Israel.
A Israeli father and his three-year-old son were lightly wounded by gunmen near Ofra in the West Bank, with a third Israeli wounded in a separate shooting incident near Ramallah.
Hamas member's shooting
Israeli troops shot dead Hamas member Yacoub Aidkadik, 28, outside his home in the West Bank city of Hebron. The army said he had tried to flee and resist arrest.
A Hamas official in Nablus, Mahmoud Ghazal, said the killing was proof that Israel had no plans for a ceasefire.
"We can't accept [Arafat's call] while Israelis are not committed to the same agreement," he said.
In an official statement, the group vowed to keep up the fight.
"We are confident we will triumph by pursuing our jihad (holy war) and our legitimate resistance to the occupation," the statement read, accusing Sharon of pursuing an "extermination campaign against our people".
The Popular Front for the Liberation of Palestine (PFLP) said Mr Arafat could not impose his decision on anyone.
"The means and the strategy of struggle are something that should be decided by all Palestinian parties," said Marwan Abdel Aal, a PFLP official based in Lebanon.
In a separate development, Israeli police detained the top Palestinian official in East Jerusalem, Sari Nusseibeh, for about an hour.
Mr Nusseibeh was taken in for questioning on Monday after ignoring an Israeli ban on a reception involving foreign diplomats for the feast of Eid al-Fitr, which marks the end of the Muslim holy month of Ramadan.
Israeli Public Security Minister Uzi Landau said that allowing Mr Nusseibeh to host the reception would have "contributed to the loss of our sovereignty in Jerusalem".
The BBC's James Reynolds in Jerusalem says Mr Nusseibeh is seen as one of the leading moderates among the Palestinian leadership.