Two Palestinians are reported to have been killed by Israeli artillery fire in northern Gaza.
Palestinian security sources said the deaths followed rocket fire into Israel by militants in the area.
However, the Israeli army had no immediate comment and it was not clear if the men killed were militants.
Earlier tonight, the Palestinian President, Mahmoud Abbas, vowed to impose law and order after the kidnapping of three Britons and a surge of unrest that has challenged his authority and could delay a crucial parliamentary vote in January.
Mr Abbas made the vow in a New Year message broadcast on Palestinian television.
In a challenge to Mr Abbas, Palestinian militant groups have repeated today that as of 1 January they would no longer be bound by a ceasefire they declared in March which has brought the quietest spell since the start of the five-year-old uprising.
Two Palestinian suicide bombings, frequent rocket attacks by Gaza militants, Israeli air and artillery strikes and West Bank arrest raids have occurred in the last month alone, adding to earlier threats to the nine-month truce.
Palestinian militants, frustrated over poverty and alleged corruption within Abbas's Fatah party and security forces, have also kidnapped foreigners and briefly seized government buildings in recent months, demanding jobs.
Three Britons kidnapped in Gaza freed
The latest of these kidnaps was that of British human rights worker Kate Burton and her parents, Hugh and Helen, who were freed yesterday.
The three, who were taken hostage by Palestinian militants in the Gaza Strip three days ago, were taken to Jerusalem by British consular officials.
Speaking following their release, Ms Burton said they had all been held in Rafah and had been treated well.
The British Foreign Office said the three were in good spirits.
Earlier, a group called the Mujahadeen Brigades issued a video denouncing Britain and saying it would free the hostages, but might take more.
Meanwhile, the Chief Palestinian negotiator, Saeb Erekat, has called for the kidnappers to be found and brought to justice.
