Mr. Bush emerged from a tour of the Yad Vashem memorial calling it a "sobering reminder" that evil must be resisted, and praising victims for not losing their faith.
Wearing a yarmulke, Mr. Bush placed a red-white-and-blue wreath on a stone slab that covers ashes of Holocaust victims taken from six extermination camps. He also lit a torch memorializing the victims.
Mr. Bush was visibly moved as he toured the site, said Yad Vashem's chairman, Avner Shalev.
"Twice, I saw tears well up in his eyes," Shalev said.
At one point, Mr. Bush viewed aerial photos of the Auschwitz camp taken during the war by U.S. forces and called Rice over to discuss why the American government had decided against bombing the site, Shalev said.
"We should have bombed it," Mr. Bush said, according to Shalev.
The Allies had detailed reports about Auschwitz during the war from Polish partisans and escaped prisoners. But they chose not to bomb the camp, the rail lines leading to it, or any of the other Nazi death camps, preferring instead to focus all resources on the broader military effort, a decision that became the subject of intense controversy years later.
Between 1.1 million and 1.5 million people were murdered at the camp.
In the memorial's visitors' book, the president wrote simply, "God bless Israel, George Bush."
Mr. Bush said later Friday, as he prepared to board Air Force One for the trip to Kuwait, that he would return to the Mideast in May to continue pressing the Israelis and Palestinians into reaching a peace agreement and to help Israel celebrate its 60th anniversary.
"There's a good chance for peace and I want to help you," Mr. Bush said, flanked by Israeli Prime Minister Ehud Olmert and Israeli President Shimon Peres at the airport here, where he boarded Air Force One, ending his visit to Israel and the Palestinian territories.
"Mr. Prime Minister and Mr. President, thank you very much for your invitation to come back. I'm accepting it now," Mr. Bush said on the tarmac.
From Israel, Mr. Bush headed to Kuwait, a tiny oil-rich nation his father fought a war over and one of only two invited guests to skip the splashy Annapolis, Maryland, rollout Mr. Bush hosted for the new U.S.-backed peace talks. Getting an Israeli-Palestinian peace pact signed would be an important milestone in Mr. Bush's presidential legacy.
However, as Brookings Institution senior fellow Michael O'Hanlon points out, "trying for Mideast peace is not the same thing as accomplishing it."
"When the president promises, or virtually guarantees this, he's raising the stakes in a way that has some potential down sides if we fail," the foreign policy analyst told CBS Early Show co-anchor Harry Smith, "because often violence follows failed negotiations."
Most people who live in the troubled region are far less optimistic of the American president's prospects for achieving lasting peace than he is himself.
CBS News correspondent Robert Berger reports a recent poll in Israel found that 77 percent of those questioned believed Mr. Bush would fail in the mission.
And one influential Palestinian lawmaker chided Mr. Bush for worrying more about his legacy than actually dealing with the issues that have plagued the region for decades. "The president, during his last days, is trying to influence his legacy and trying to salvage the disastrous American policy in the region," said Hanan Ashrawi.
The Holocaust memorial was closed to the public and under heavy guard Friday, with armed soldiers standing on top of some of the site's monuments and a police helicopter and surveillance blimp hovering in the air overhead.
"I was most impressed that people in the face of horror and evil would not forsake their God. In the face of unspeakable crimes against humanity, brave souls - young and old - stood strong for what they believe," Mr. Bush said.
"I wish as many people as possible would come to this place. It is a sobering reminder that evil exists, and a call that when evil exists we must resist it," he said.
It was Mr. Bush's second visit to the Holocaust memorial, a regular stop on the visits of foreign dignitaries. His first was in 1998, as governor of Texas. The last U.S. president to visit was Bill Clinton in 1994.
Mr. Bush, making the most extensive Mideast trip of his presidency, was accompanied on his tour by a small party that included Rice and Israeli Prime Minister Ehud Olmert.
At the compound, overlooking a forest on Jerusalem's outskirts, Mr. Bush visited a memorial to the 1.5 million Jewish children killed in the Holocaust, featuring six candles reflected 1.5 million times in a hall of mirrors. At the site's Hall of Remembrance, he heard a cantor sing a Jewish prayer for the dead.
Shalev presented Mr. Bush with illustrations of the Bible drawn by the Jewish artist Carol Deutsch, who perished in the Holocaust.
Deutsch created the works while in hiding from the Nazis in Belgium. He was informed upon, and died in 1944 in the Buchenwald camp. After the war, his daughter Ingrid discovered that the Nazis had confiscated their furniture and valuables but had left behind a single item: a meticulously crafted wooden box adorned with a Star of David and a seven-branched menorah, containing a collection of 99 of the artist's illustrations of biblical scenes.
The originals are on display at Yad Vashem. The memorial recently decided to produce a special series of 500 replicas, the first of which was to be presented to Mr. Bush.
Debbie Deutsch-Berman, a Yad Vashem employee whose grandfather was Deutch's brother, said she was proud that Mr. Bush would be given her relative's artwork.
"These are not just his paintings, they are his legacy, and the fact that they survived shows that as much as our enemies tried to destroy the ideas that these paintings embody, they failed," she said.