The killing rekindled tensions between Yasser Arafat's Palestinian Authority (PA) and the Islamic opponents of peace with Israel, which were provoked by last October's Wye Agreement. Mr Arafat, who is in Washington this week urging President Bill Clinton to make Israel complete its promised West Bank withdrawal, is eager to show he is cracking down on the men of violence.
Captain Rafat Jouda, their latest victim, noticed the wanted men in the Sinai border town of Rafah and gave chase. A police spokesman said the captain opened fire when they refused to stop. The three shot back, fatally wounding him and an eight-year-old girl.
They were captured later in the Shati refugee camp. The men were identified as Ra'ed el Attar, Osama Abu Taha and Mohammed Abu Shamala. They appeared on a list of alleged killers presented by Israel to the PA during the Wye negotiations. They are accused of belonging to Hamas's military wing, Ezzedin al-Qassam.
Palestinian police later arrested dozens of Hamas protesters who stoned a police station. At the same time, the Hamas leader, Sheikh Ahmed Yassin, launched a hunger strike in sympathy with Hamas activists held without trial.
Israel's Prime Minister, Benjamin Netanyahu, has frozen the Wye accords until after the election. He launched his re-election campaign this week under the slogan "A strong leader for a strong people". The three-month deadline for completing the current West Bank redeployment expired at the weekend with Israel still holding 11 of the 13 per cent of land it was due to hand over.
Mr Netanyahu justified the delay by accusing Mr Arafat of freeing 21 prisoners serving sentences for murdering Israelis and Americans.
Yediot Aharonot, Israel's biggest-selling daily newspaper, challenged Mr Netanyahu's contention that the PA is operating a "revolving door".
It said 197 Hamas activists had been arrested since October and were still being held in Palestinian prisons.