Dennis McDonough, White House deputy national security adviser, said the Obama administration is working with NATO allies to "increase resources both as it relates to troops, but also as it relates to trainers, as it relates to civilian capacity, and as it relates to economic investment and assistance" in Afghanistan.
McDonough said the White House expects "some progress," but cautioned that it is an "ongoing process."
Michael O'Hanlon of the Brookings Institution said it will be a big challenge for the Obama administration to persuade NATO countries to contribute more troops on the ground in Afghanistan.
"They're not going to be doing much. I can predict no more than a few hundred or maybe a couple thousand additional troops at most. It's going to be a big challenge," O'Hanlon said.
Obama finishes his trip with a stop in Turkey, a Muslim nation, where he will stress that Turkey is a vital member of the NATO alliance and a close ally of the United States. Relations with Turkey have been strained since the start of the Iraq War in 2003 and administration officials hope the visit will smooth over tensions.
"We share a commitment to democracy, a secular constitution, respect for religious freedom and belief and in free market and a sense of global responsibility," Secretary of State Hillary Rodham Clinton said in early March when she announced the president's stop in Turkey.
In Ankara, Turkey, Obama will meet with President Abdullah Gul and Prime Minister Recep Tayyip Erdogan.
Obama will travel to Istanbul where he will hold a series of meetings with cultural leaders and a roundtable with students. The White House said this roundtable will give Obama a chance to speak to young people in Turkey, across Europe and in Southwest Asia. He will use video technology.
Obama will deliver two major speeches: one in Strasbourg, France, focusing on the trans-Atlantic alliance and another in Prague focusing on proliferation challenges.
They may not all agree with Obama, but world leaders are lining up to meet with him.
In addition to the G20 summit and NATO and EU meetings, Obama goes to Europe with a busy schedule of one-on-one meetings with a host of world leaders including British Prime Minister Gordon Brown, President Dmitriy Medvedev of Russia, President Hu Jintao of China, Prime Minister Manmohan Singh of India, President Lee Myung-bak of South Korea and King Abdullah of Saudi Arabia.
Obama will meet with David Cameron, the leader of the Conservative Party in Britain. And in Prague he will meet with former Czech President Vaclav Havel
ABC News polling director Gary Langer and Sunlen Miller contributed to this report.