"Our hope for peace for boys and girls everywhere extends across the world, especially in the Middle East," the president said before the start of a T-ball game at the White House.
"Today's actions in the Middle East remind us that friends and allies must work together for a sustainable peace particularly for the sake of children," Bush told the teams of youngsters and visitors.
As he was leaving the White House to fly to Florida, the president added that "America mourns the loss of innocent life, those tragic occasions when innocent people are killed. Our sympathies go out to those who lost their lives today, who lost their lives throughout this crisis."
He said the United States "is resolved to work with members of the United Nations Security Council to develop a resolution that will enable the region to have a sustainable peace. A peace that stands. A peace that will enable mothers and fathers to raise their children in a hopeful world.
"May God bless those who lost their lives," Bush said.
The president said he spoke with Secretary of State Condoleezza Rice, who was in Jerusalem, twice on Sunday and also had a telephone conversation with British Prime Minister Tony Blair, who was in California.
Israel's attack killed more than 50 people, about half of them children, in the southern Lebanon village of Qana.
Earlier, Bush's aides and U.S. officials insisted anew on the need for a long-term solution to end the fighting.
"The key here is that we want a cease-fire that will work," White House press secretary Tony Snow told reporters.
Before leaving for church, Bush heard from his national security adviser at 6:40 a.m. about the attack.
"This clearly was a terrible thing," Snow described the president as saying.
Bush, who was heading to Florida late Sunday, was sticking to his approach for a lasting settlement for the region.
"The president's main concern is to keep moving on a credible, diplomatic track," Snow said. "He wants a resolution that will solve the problem. We want the Lebanese forces to move in. We want the militias to move out, or stop acting as independent militias."
Snow said the Qana attack "was a horrible event. ... It's really important to remove the conditions that led to that."
He acknowledged it "clearly does have an impact" on hastening efforts to end the fighting, triggered by Hezbollah's cross-border raid from Lebanon into Israel and the capture of two Israeli soldiers.
In addition, a White House spokesman, Blair Jones, said the U.S. was urging the Israeli government "to exercise the utmost care so as to avoid any civilian casualties. This tragic incident shows why this is so critical."
Snow said the United Nations should pass a resolution that is intended to "get independent actors out of southern Lebanon."
Meantime, the State Department's third-ranking official expressed optimism that a political settlement could be reached despite the airstrike.
Nicholas Burns said the U.S. was committed to securing a cease-fire between Israelis and Hezbollah militants, focusing on a multinational force in the region. Snow said talks at the United Nations about troop contributions would not begin until Tuesday or Wednesday.
"This is a very sad day. We are working toward that cease-fire," Burns said. "We are close to a political agreement between Israel and Lebanon to end this fighting."
Burns said he think there will be "enormous pressure on Hezbollah by all the other elements of the Lebanese government to agree to stop this fighting."
Members of Congress said they supported firm U.S. backing for Israel.
"I know some in the world have called for an immediate cease-fire," said Sen. Chuck Schumer, D-N.Y. "But that says Hezbollah has a gun to Israel's head; let's let them continue to keep the gun there which they can use at will. It's just not fair to Israel."
Added Sen. Mitch McConnell, R-Ky.: "Israel needs a strong supporter. It certainly doesn't have any in the neighborhood."
Burns appeared on "FOX News Sunday" and ABC's "This Week." Schumer and McConnell were on another cable network.