Four Hamas members were killed by Israel on Tuesday
There was an exchange of fire and the two Palestinians were hit by a tank shell, the Israelis said.
Palestinian security sources said the Israeli army told them they were ready to hand over the bodies of the two men.
Witnesses said at least two missiles hit the car.
Security sources named the dead man as Baker Hamdan, 30. Hospital officials said two other passengers in the car were wounded.
The latest violence incident in the region came as Israeli Prime Minister Ariel Sharon accepted an invitation by US President George W Bush to meet in Washington on 7 February.
Israel's controversial policy
Thursday's helicopter gunship attack appears to be in line with Israel's recent policy of targeting militants it says are planning or involved in attacks on Israelis.
It followed a shooting spree on Tuesday by a Palestinian gunman who killed two Israeli women in Jerusalem's city centre.
The Israelis say Hamdan had been involved in the recent killing of four Israeli soldiers at an army post in Gaza and was planning more attacks.
The army said he had been arrested briefly by Palestinian police but was then released.
Three other Palestinians were killed earlier on Thursday, two in an explosion in Gaza and a third in a clash with Israeli soldiers in the West Bank town of Ramallah.
The Popular Front for the Liberation of Palestine (PFLP) claimed responsibility for what it described as a suicide operation in Gaza in which two militants died.
The attempted attack was in response for Israel's "assassination of four martyrs" in the West Bank town of Nablus on Tuesday, the PFLP said.
Palestinian security officials said a Palestinian intelligence officer died in a gun battle with Israeli troops in Ramallah, where Israeli tanks encircle the headquarters of Palestinian leader Yasser Arafat.
Pressure on Arafat
Palestinian leaders have appealed for international intervention, saying they cannot enforce a ceasefire while West Bank towns remain under siege and Israel continues to kill suspected militants.
And Mr Bush has now invited Mr Sharon to meet in Washington.
It will be Mr Sharon's second visit to the United States in just over two months, whereas Mr Arafat has not yet met the US president since he took office a year ago.
Parliamentary invitation
The speaker of the Palestinian parliament, Ahmed Qureia, warned on Thursday that the violence could lead to "a generalised disaster".
Mr Qureia invited Israel's parliament speaker, Avraham Burg, to address the Palestinian legislature, after meeting in France with Mr Burg and with Israeli Foreign Minister Shimon Peres - both dovish members of the moderate Labor party.
Mr Burg said he would accept the invitation and go to Ramallah if it was legal under Israeli regulations.
But Israel's Defence Minister, Binyamin Ben Eliezer, said he intended to ban Mr Burg from going to Ramallah.
"Like all Israelis who head to the Palestinian territories, Avraham Burg must receive permission from the army," Mr Ben Eliezer said on public television.
The Palestinian intelligence chief, General Tawfiq Tirawi, contacted the television station and said: "Burg does not run any risks and he will be received with open arms."