BRUSSELS — President Barack Obama has spent much of his presidency mired in the challenges of a world well outside the borders of Europe — the turmoil of the Middle East, the power struggles in Asia and the terrorist threats percolating in northern Africa, Pakistan and elsewhere.

But Russia’s invasion of Ukraine and its stunningly fast annexation of Crimea have demanded a renewed focus on a part of the world that dominated U.S. attention in the 20th century.

Often accused of neglecting Europe in his first five years in office, Obama is using his trip here to recommit to the NATO alliance, rally the continent against Russian “brute force” and cast the showdown as a test of common values.

To show resolve, Obama decided on Wednesday to modestly increase military deployments in Eastern Europe, and aides said he would intensify efforts to broaden energy security, negotiate a trade agreement with Europe and upgrade military capabilities.

Yet it will be hard to back up words with resources. The U.S. has only a fraction of the force it once had in Europe, expanded energy ties will take years and his own party leaders oppose quick action on a new trade pact.

Moreover, Obama next month will head back to Asia, where aides said he will again promote his policy of pivoting toward the region he believes represents the future. One goal then for Obama, aides said, is to challenge Europe to take more of a leadership role itself, a familiar theme from Washington but one infused with new urgency by the Ukraine crisis.

“Russia’s leadership is challenging truths that only a few weeks ago seemed self-evident,” Obama said in a speech here on Wednesday. “That in the 21st century, the borders of Europe cannot be redrawn with force; that international law matters; and that people and nations can make their own decisions about their future.”

“The contest of ideas,” he added, “continues.”

Julianne Smith, a former national security aide in Obama’s White House now at the Center for a New American Security, said she did not expect “a fundamental recalibration of U.S. foreign policy” toward Europe, but a more “symbolic” shift.

But Russia’s actions in Ukraine appear to have sent an electric jolt through Obama and his team.

At first, when a political crisis broke out in Kiev in November, he largely left the matter to Vice President Joe Biden. Since President Vladimir Putin ordered troops to seize Crimea, Obama has become increasingly engaged, blitzing foreign leaders with telephone calls, imposing sanctions and speaking out more frequently.

To reassure nervous allies, he sent six extra F-15C Eagles to Lithuania and 12 F-16 fighter jets to Poland.

Obama’s speech here on Wednesday offered his most extensive rejoinder yet to Russia, a point-by-point refutation of every justification offered by Moscow for its seizure of Crimea. He rejected Putin’s comparison of his actions in Crimea to the West’s actions in Kosovo. He said Kremlin claims of persecution of Russian speakers in Ukraine were not true and called it “absurd” to suggest America supported fascists in Kiev.