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 Obama will have no choice but to address. For months, decisions on a number of festering problems areas have been deferred by administration officials until after the election. And yet as Richard Nixon did in opening ties to China or Ronald Reagan in embracing arms control, 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 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.

'Deft and subtle'

While Obama can scarcely hope for something as seminal as Nixon's journey to Beijing, experts say he has the chance to forge a new relationship with China that takes into account its rising economic might. Last year, the president articulated a "strategic pivot" from the Middle East to China and Asia. Critics said there was less to the initiative than met the eye. But with four more years, Obama could put meat on the bones of an ambitious, if incomplete, policy.

To be credible in Asia, experts said, the United States will need a robust military presence from the Yellow Sea to the South China Sea. But unless the White House and Congress strike a fiscal deal, the Pentagon will face deep budget cuts, depriving it of the ability to project such power. The challenge will be to assert a big role without precipitating a clash with Beijing. "It's going to have to be very deft and subtle in its implementation because there's going to be pushback from the Chinese," said Nicholas Burns, a former undersecretary of state who teaches at Harvard.

Putin changes tone

There may also be an opening for Obama with Russia on one of his most cherished issues: nuclear nonproliferation. Among the most intriguing congratulatory telegrams the president received was from President Vladimir Putin, who had taken a bristling tone toward the United States for much of the last year. On Wednesday, Putin and his surrogates signaled a willingness to make deals.

In his infamous remark to then-President Dmitry Medvedev last March, Obama promised "flexibility" after the election on a missile defense system based in Europe -- a concession Putin, who succeeded Medvedev last May, has long sought.

For Obama, the Middle East is generally less a landscape for bold new initiatives than a place for triage. On situations as varied as the crackdown in Syria and the Muslim Brotherhood government in Egypt, Obama will have to fight to keep intact even the vestiges of the overture he made to the Islamic world early in his presidency.

But other unfinished business remains there -- not least Obama's frustrated efforts to broker a peace agreement between Israel and the Palestinians. But several experts expressed doubt that the president would thrust himself again into the role of Middle East peacemaker.

Prime Minister Benjamin Netanyahu of Israel, who has had a fraught relationship with Obama, seems likely to stay in power with a right-wing government. "Because he got his fingers burned and was outmaneuvered by Netanyahu, he will wait to see the outcome in the Israeli election," said Martin Indyk, a former U.S. ambassador to Israel. Obama will not be able to avoid one issue.

Over U.S. and Israeli objections, the Palestinian Authority's president, Mahmoud Abbas, also known as Abu Mazen, is likely to petition for nonstate membership in the United Nations next month. If the U.N. were to grant that, it would cause Congress to cut off aid not only to the Palestinian Authority but also to the U.N.