Israeli officials said more than 100 missiles had been fired from Gaza at Israeli targets in and outside the Gaza Strip, killing one woman and injuring several others.
Ariel Sharon, the Israeli prime minister, said his security forces should show no restraint in suppressing the fire if the authority failed to do so.
The Palestinian leader, Mahmoud Abbas, pledged last night that the authority would "do our utmost" to stop the attacks. An Israeli invasion would "sabotage everything", he said.
"We are determined to stop the launching of the homemade rockets, whatever the price ... I cannot promise how much time it will take me."
Mortars and rockets contin ued to hit Israeli areas but at a much reduced rate as Palestinian police began to exert control and Hamas pulled back from a direct confrontation with the authority and Israeli troops. Israel maintained its pressure on Gaza, killing one Hamas member and hitting several Hamas targets with missiles.
Palestinian police pressed home the advantage they gained on Friday by removing the flags of Hamas and Islamic Jihad from buildings. On Friday two people were killed in the crossfire as Hamas militants resisted a Palestinian Authority crackdown.
A Hamas official told reporters last night that the group did not want to cause divisions within the Palestinian Authority, but it retained the right to retaliate against Israeli attacks. "We are committed to a conditional calm," he said.
In Gaza, residents were preparing for Israeli military action, speculating that it might begin when Condoleezza Rice, the US secretary of state, leaves after a short visit this week. Israel stopped all movement between the north, centre and south of Gaza and prevented men between the ages of 18 and 35 from crossing the border into Egypt.
Mr Abbas, who is in Gaza, made a televised speech at the weekend in which he reiterated his call for a single authority and a single armed force for Palestinians.
Yesterday morning, Israel assassinated a Hamas activist in Khan Yunis in the Gaza Strip. Said Sayam was said to be walking to the home of his father-in-law when he was shot in the chest and the neck. Witnesses said the shots had been fired from an Israeli military watchtower.
During the day four missiles were fired at the Israeli town of Sderot and several mortars were fired at Gush Katif. One hit a home, injuring five people.
At Israel's weekly cabinet meeting, Shaul Mofaz, the defence minister, said that Israel would launch a "massive, prolonged and intricate" military strike if the Palestinian Authority did not stop the firing.
Mushir Masri, a Hamas spokesman in Gaza, told reporters an Israeli incursion would cause more violence. "They should understand that by this serious escalation they have opened the gates of hell, and if they enter Gaza we are not going to stand by silently."
Israel has never managed to stop the firing of missiles by direct force. Militants have stockpiles of mortars and missiles all over the Gaza Strip. Israel's big fear is that its forces could be targeted by missiles when they deploy in large numbers to evacuate residents of Gush Katif in mid-August.
Its forces are also under pressure from opponents of disengagement. Yesterday there were scuffles at the Kissufim checkpoint, as soldiers tried to prevent settlers from going to Gush Katif. Nine soldiers refused to obey orders to stop passage at the checkpoints and two absconded to join the settlers in Gush Katif.
