Bush and Condoleezza Rice, the US secretary of state, plan to meet Danilo Turk, the Slovenian president, and Janez Jansa, the prime minister, on Tuesday.
Later they will meet Jose Manuel Barroso, the European Commission president, and Javier Solana, the EU foreign policy chief, at a castle that Josip Broz Tito, the late Yugoslav leader, once used as a retreat.
He also has planned stops in Germany, Italy, the Vatican, France, England and Northern Ireland.
Range of issues
Dimitrij Rupel, the Slovenian foreign minister, said the EU and US officials would discuss a wide range of issues including the Middle East peace process, global warming and security, efforts to forge a new global trade agreement, Iran's nuclear programme, the food-price crisis and tensions with Serbia over Kosovo's independence.
The two sides also were to discuss ways to improve airline safety and broaden a programme that lets people travel in the US without visas for up to 90 days.
The visa waivers currently are available for only 15 of the EU's 27 member nations.
Officials said the one issue they hoped could be resolved was a long-running dispute over an EU ban on imports of US poultry.
Although Bush will meet major European leaders again at next month's summit in Japan of the group of eight major industrialised nations, the Europe is likely to be his last tour across the continent before the US presidential elections in November.
Bush's Slovenia visit prompted tough security measures, with Ljubljana airport saying that any movement of vehicles or people would be prohibited 15 minutes before Air Force One was scheduled to touch down on Monday.
The Slovenian government also agreed with the US to temporarily deploy American forces to protect Bush against the threat of an air attack.