A missile and rocket exchange between Hamas militants and Israeli forces has immediately challenged the partial Gaza ceasefire announced unilaterally by Prime Minister Ehud Olmert last night.
The ceasefire came into effect at 02.00 today. Israel says it will not pull troops out at present and will continue to attack opponents as necessary. Hamas says it will not accept an Israeli presence in Gaza and wants an end to the blockade.
In a televised address, Mr Olmert warned militants in Gaza that if they "decide the blows they've been dealt are not sufficient and they are interested in continuing the fight, Israel will be prepared for such and feel free to continue to react with force".
Palestinian President Mahmoud Abbas, who has forthrightly opposed Israeli action but is also a political opponent of Hamas, Mr Abbas said the ceasefire was "important and necessary but insufficient", and called for a complete withdrawal of Israeli troops from Gaza.
Israel has begun pulling some of its troops out of the territory, says the BBC's Katya Adler in Jerusalem.
United Nations secretary general Ban Ki Moon says that this needs to continue. He said last night he was relieved about an Israeli ceasefire in the Gaza Strip and urged Israel to withdraw all of its troops as soon as possible.
"I am relieved that the Israeli government has decided to cease hostilities as of midnight GMT," Ban told reporters. "This should be the first step leading to the full withdrawal of Israeli troops from Gaza," he said, adding that he wanted the withdrawal "as soon as possible".
The UN leader said that Hamas militants also needed to do their part to bring an end to the violence by halting their rocket attacks against southern Israel.
"Hamas militants must stop firing rockets now," he said.
Ban added that humanitarian access for the people of the Gaza Strip was the top priority and the United Nations was ready to act immediately.
"Any durable solution must include the reopening of the (Gaza border) crossings and the prevention of illicit trafficking in arms," he declared.
Ban flies to Damascus on Sunday to meet with Syrian President Bashar al-Assad before heading to the Egyptian Red Sea city of Sharm el-Sheikh for a summit meeting on aid and reconstruction efforts for Gaza hosted by Egypt's President Hosni Mubarak.
Israel accuses Syria and Iran of supporting and arming Hamas, an accusation they deny.
Ban said he and European leaders including French President Nicolas Sarkozy, British Prime Minister Gordon Brown and German Chancellor Angela Merkel would discuss "how to make this ceasefire durable and sustainable".
One of the priorities, he said, was ending the smuggling of weapons to Hamas, many of which are transferred via tunnels under the Egyptian border with Gaza.
"We will also seriously consider to bring this Middle East peace process back (on) track, particularly as we are expecting a new US administration in just a couple of days," he said.