"Another one-way ceasefire that leads to rocket attacks on Israel is not acceptable," Bush said in his first public comments on the fighting.
The United States has demanded Hamas, which it considers a terrorist organization, take the first step by halting rocket attacks on Israel.
"And promises from Hamas will not suffice - there must be monitoring mechanisms in place to help ensure that smuggling of weapons to terrorist groups in Gaza comes to an end," Bush said in remarks prepared for his regular Saturday radio address, which was taped and released on Friday.
The United States has defended Israel's right to respond to the rocket attacks and has blamed the renewed fighting on Hamas, the militant group that seized control of the Palestinian territory about 18 months ago.
At least 429 Palestinians have been killed in the seven days of fighting and some 2,000 have been wounded. Rockets fired from Gaza have killed four Israelis.
A Palestinian official has told Reuters that Egypt had begun exploratory talks with Hamas to stop the fighting.
Working the phones
Bush and US Secretary of State Condoleezza Rice have been engaged in telephone diplomacy during the past week, talking with leaders in the Middle East and Europe, including Prime Minister Ehud Olmert and Palestinian President Mahmoud Abbas.
Earlier on Friday the White House said Israel must decide for itself whether to go into the Gaza Strip with ground forces but it cautioned any actions should avoid civilian casualties and ensure the flow of humanitarian goods.
Bush also expressed concern about the humanitarian situation in Gaza and said the United States has offered $85 million to relief efforts this week. He criticized Hamas for using its resources on rocket launchers instead of roads and schools.
"Hamas has demonstrated that it has no intention of serving the Palestinian people," Bush said.
Rocket launched frol Gaza towards Israel (Photo: Reuters)
He also urged other countries to pressure Hamas to stop its rocket attacks on Israel and support the elected Palestinian leaders.
"I urge all parties to pressure Hamas to turn away from terror and to support legitimate Palestinian leaders working for peace," Bush said.
Rice told reporters after meeting Bush that the United States was working toward a "durable and sustainable" ceasefire in Gaza but that she had no plans at this point to travel to the Middle East to try to broker one.
"We are working toward a ceasefire that would not allow a re-establishment of the status quo ante where Hamas can continue to launch rockets out of Gaza," Rice said.
With less than three weeks before leaving office, Bush said he was keeping his successor, President-elect Barack Obama, and his team informed.