Bush was speaking at a hastily arranged news conference at the White House in which he also touched on the fighting in Iraq and negotiations with Iran.
On Lebanon, Bush said on Monday: "The need is urgent. The international community must now designate the leadership of this new international force, give it robust rules of engagement and deploy it as quickly as possible to secure the peace."
United Nations resolution has authorised up to 15,000 UN peacekeepers to help an equal number of Lebanese soldiers extend their authority into south Lebanon as Israel withdraws.
The UN wants 3,500 troops on the ground by next Monday, but so far, no European country has offered large numbers of troops.
France which commands the existing UN peacekeeping force there, the United Nations Interim Force in Lebanon (Unifil), had been expected to make a significant new contribution that would form the backbone of the expanded force.
However, Jacques Chirac, the French president, has offered just 200 army engineers – despite saying that France should command the 15,000 strong international mission.
"I would hope that they would put more troops in," Bush said of France's commitment.
"Wars are not a time of joy. These are challenging times and difficult times"
George Bush, US president
France was an enthusiastic supporter of the UN resolution which authorised the peacekeeping force.
Bush said the US would give an additional $230 million in aid to Lebanon.
No Iraq pullout
Bush also said that the war in Iraq, with daily bombings and US casualties now standing at more than 2,600 was "straining the psyche of our country".
"Sometimes I'm frustrated. Rarely surprised. Wars are not a time of joy. These are challenging times, and difficult times," he said.
He conceded that the war had become a major issue in this year's mid-term congressional elections.
Bush said that if Iraq's government there fails, it could turn the country into a "safe haven for terrorists and extremists" and give those opposed to the US-led presence revenues from oil sales.
"It would be wrong, in my judgment, to leave before the mission is completed in Iraq"
George Bush, US president
"I hear a lot of talk about civil war. I'm concerned about that, of course, and I've talked to a lot of people about it. And what I've found from my talks are that the Iraqis want a unified country. And that the Iraqi leadership is determined to thwart the efforts of the extremists and the radicals," Bush said.
Bush also said he was troubled that so many US House and Senate candidates were calling for the withdrawal of US forces from Iraq.
"There are a lot of good decent people saying 'get out now. Vote for me, I'll do everything I can to cut off money...' It's a big mistake. It would be wrong, in my judgment, to leave before the mission is completed in Iraq," he said.
In early August the US army in Iraq launched a major operation in Baghdad to wrest streets back from sectarian militias and prevent further violence between Iraq's ruling Shia Muslims and the country's Sunnis.
More than 3,500 Iraqis were killed last month, the highest monthly civilian toll since the war began.