WASHINGTON — If history is any guide, President Obama will cast his eye abroad over the next four years, hoping to put an imprint on the world that matches the sweeping domestic programs of his first term. From Iran and Russia to China and the Middle East, there are plenty of opportunities, but also perils, for a leader seeking a statesman’s legacy.

Many of the issues Mr. Obama will have no choice but to address. For months, decisions on a number of festering problem areas have been deferred by administration officials until after the election. And yet as Richard M. Nixon did in opening ties to China or Ronald Reagan in embracing arms control, Mr. Obama could see the foreign policy arena as a place to achieve something more lasting in a second term than crisis management and more satisfying than the gridlock that has bedeviled his domestic initiatives.

Atop Mr. Obama’s list, administration officials and foreign policy experts agree, is a deal with Iran to curb its nuclear program. The United States is likely to engage the Iranian government in direct negotiations in the next few months, officials said, in what would be a last-ditch diplomatic effort to head off a military strike on its nuclear facilities.