The president is also visiting Romania, Croatia and Russia in a trip built around the NATO summit in Bucharest, Romania.
Addressing reporters, Bush said Congress should pass a free-trade deal with Colombia, a law to modernize the Federal Housing Administration, and an update to a law allowing eavesdropping on suspected terrorists.
"These are all vital priorities," Bush said. "I ask members of both parties to get these important pieces of legislation to my desk as soon as possible."
The intelligence law Bush wants would make it easier for the government to spy on foreign phone calls and e-mails that pass through the United States.
He will accept only a version that gives legal protection to telecommunications companies that helped the government wiretap U.S. computer and phone lines after the Sept. 11 terrorist attacks without clearance from a secret court. Some lawmakers object to give the companies that level of legal immunity.
"Our intelligence professionals are waiting on Congress to give them the tools they need to monitor terrorist communications," Bush said.
Bush said the housing law he wants would allow more struggling homeowners to refinance their mortgages. He said the trade pact with Colombia is an important way of helping a South American ally and businesses in the United States.
The president took no questions.
On his trip, Bush is promoting NATO expansion and trying to shore up ties with allies. But many world leaders have begun looking beyond him as his second White House term winds down.
Bush is beginning with a stop in Ukraine to tout that country's democratic reforms.
The president then goes to Romania for his last summit with NATO leaders, where the alliance's membership and the war in Afghanistan will be key topics.
Bush is also scheduled to visit Croatia and head to Russia for what will likely be his final meeting with Vladimir Putin as Russian president. Bush hopes to break a logjam between the two nations over a proposed U.S. missile defense system; Putin's successor takes over in May.
The agenda is part of the busiest travel year in Bush's presidency. He went to the Middle East in January and to Africa in February. After his current trip, Bush has five more major excursions on the books -- from Europe to Asia, the Middle East to South America.
Bush remains relevant to the end of his term as commander in chief. But some world leaders have begun to calculate how far they should commit to a president whose days are numbered and whose legacy had been tarnished by the war in Iraq. The 2008 U.S. presidential race is grabbing attention overseas.
At NATO, Bush is seeking to expand the alliance to include three Balkan countries -- Albania, Croatia and Macedonia. He also wants Ukraine and Georgia to be on track for membership, but that idea faces stiff resistance from Putin, who sees it as a threat into Russia's former sphere of influence.
But Bush sees NATO expansion as a way to cement democratic gains in Europe.
The United States and its NATO allies remain broadly united about the war in Afghanistan, but there has been trans-Atlantic bickering on how to proceed, too.