If the suspicions prove correct, it would be the first time Arab citizens of the Jewish state have been so directly involved in an apparent suicide car-bombing attempt, security experts said.
Police said five people had been arrested. An Israeli court ordered them held for 11 days pending an investigation.
Israel's domestic Itim news agency said the five were members of a single family and were suspected of a link to the two attacks. It said they denied any connection.
One car blew up in the Sea of Galilee resort of Tiberias on Sunday, killing the two men inside the vehicle. A few minutes later another car exploded in the northern port city of Haifa, killing its occupant.
The security sources said police believed two of the men who died in the explosions were from the Israeli Arab village of Daburiya, near Tiberias.
A resident of the village said the men's parents had been taken away Monday for DNA testing to try to confirm the identities of the remains.
The resident named the two suspects as Amir Masalcha, 24, and Jad Azaiza, 23, both members of the Islamic Movement, a fundamentalist religious group in Israel. There was no immediate word on the identity of the third man.
Israeli newspapers, bound by a court gag order, had dropped heavy hints Monday that Israeli Arabs were involved in the two incidents.
At a hearing on whether to lift the gag order, a Tiberias judge allowed publication of news that police had presented secret evidence of what the judge called a "time bomb" which warranted continued imposition of the order.
The blasts occurred less than 24 hours after Israeli Prime Minister Ehud Barak and Palestinian President Yasser Arafat signed a revised land-for-security deal dubbed "Wye Two" in Egypt's Red Sea resort of Sharm el-Sheikh.
Arafat told reporters in Gaza he had spoken by telephone with Barak after the explosions to condemn what the Palestinian leader called "sabotage operations that should be countered."
His cabinet later approved the Wye Two deal by a majority and made clear it would not tolerate attempts by internal opponents to try to derail the peace process with violence.
"The leadership reiterates its commitment to signed agreements and it will not allow tampering hands to deal a blow to our national gains," a cabinet statement issued by the official Palestinian news agency WAFA said.
No one immediately claimed responsibility for the blasts that were reminiscent of past attacks by Hamas and Islamic Jihad, fundamentalist groups which oppose peace moves between Israel and Arafat's Palestine Liberation Organization.
Israeli Deputy Defense Minister Ephraim Sneh said it was possile that Palestinian Islamic militant organizations, having a hard time operating in the West Bank and Gaza Strip, had drawn some Arab citizens of Israel into their ranks.
He said he believed only a handful of Israel's Arab citizens would answer such a call. One in five Israelis is an Arab.