He also planned to seek support on climate change and to boost trade, although no major agreements are expected to result before his term ends in January.
"I don't think you're going to see any dramatic announcements," national security adviser Stephen Hadley told reporters last week, according to the Agence France-Presse.
In addition to the summit in Slovenia, the president's week-long tour will take him to Germany, Italy, France, England, Northern Ireland and the Vatican.
Iran's nuclear program is one of the top agenda items. Britain, France and Germany -- backed by China and the United States -- are preparing to offer new economic and diplomatic incentives for Iran to halt uranium enrichment, and Tehran is planning a counter-offer, Hadley said.
President Bush recently met with Israeli Prime Minister Ehud Olmert, and media reports said the Israeli leader was pushing Washington to plan for a use of force.
"If Iran continues its nuclear program, we will attack it," an Israeli deputy prime minister, Shaul Mofaz, was quoted as saying in the Yediot Aharonot daily on Friday, reported AFP. Olmert later distanced himself from the comments.
Also on the agenda is aid to Afghanistan. A donors' conference is set for June 12 in Paris, and President Bush hopes to press U.S. allies to make good on previous aid pledges.
He also plans to discuss the Mideast peace process, relations with Russia, promoting democracy in Lebanon, and engaging Syria, according to the AFP.
On climate change, Hadley said the president will encourage greater European cooperation for his approach, which would include binding commitments from major emerging economies such as India and China. Critics have called the plan a U.S. effort to dodge existing international frameworks for reducing greenhouse gas emissions.
Before leaving Washington, Mr. Bush told reporters that the economy will also be discussed.
"A lot of Americans are concerned about our economy. I can understand why," he said. "Gasoline prices are high; energy prices are high. I do remind them that we have put a stimulus package forward that is expected to help boost the economy. And of course, we'll be monitoring the situation."
President Bush also said that he would discuss ways to become less-dependent on fossil fuels, but reiterated his controversial calls to drill in the Arctic National Wildlife Refuge and other areas.
"I've proposed to the Congress that they open up ANWR, open up the Continental Shelf, and give this country a chance to help us through this difficult period by finding more supplies of crude oil, which will take the pressure off the price of gasoline," he said.
Next month, President Bush is scheduled to visit Japan, and in August attend the Olympic Games in Beijing, China.