After a presidential campaign waged on the domestic terrain of jobs and economic growth, President Barack Obama is confronted by a volatile international environment that will help determine whether he can keep his promise to restore America’s prosperity.

Israel is threatening to attack Iran’s nuclear facilities, a move that would roil oil markets and draw U.S. military support for the Jewish state. The promise of the Arab Spring has given way to concerns about the future of the new democracies, and Islamic extremists threaten Afghanistan, Pakistan, Yemen and a swath of North Africa.

China, the largest holder of U.S. debt, is undergoing a generational change in leadership and flexing its muscles toward its neighbors. Despite Obama’s first-term effort to improve ties with Russia, the relationship remains prickly. While the U.S. economy is recovering slowly, America’s European allies are mired in a financial crisis that threatens the global economy.

“The world has become a global market where bad debt, higher oil prices and defaulting economies travel far, fast and wide,” said Aaron David Miller, an analyst at the Woodrow Wilson Center for International Scholars in Washington. “The problem is that a president has very little control over those factors,” even though he must mitigate their effects.

Obama will confront diverse security challenges with a shrinking defense budget that will force choices among costly weapons systems that create jobs and boost local economies, but may not be as well-suited to 21st Century warfare as less expensive cyber weapons and special operations forces.

New Dangers

There are new dangers, too, from the effects of climate change to cyberattacks by foreign intelligence agencies, independent hackers and criminal groups.

Many of the U.S. economic crises over the last century were brought on wholly or in part by conflicts with adversaries abroad, said Michael O’Hanlon, a national security specialist at the Brookings Institution, a Washington policy center.

From the 1930 Smoot-Hawley tariffs that helped deepen the Great Depression to the oil embargo that accompanied the 1973 Arab-Israeli War to the last decade’s wars in Iraq and Afghanistan that added a couple trillion dollars to the federal deficit, history shows that foreign policy can’t be an afterthought, O’Hanlon said.

Obama will handle the international issues with a revamped national security team including a new secretary of state and perhaps defense secretary. Susan Rice, the U.S. ambassador to the United Nations, is emerging as the favored candidate to succeed Secretary of State Hillary Clinton, according to six current or former White House official who spoke on the condition of anonymity to discuss internal deliberations.

Here are some of the major national security issues that continue to percolate as Obama savors his election win:

Defense Spending

One of Obama’s most immediate tasks will be to avert automatic spending cuts that will take effect Jan. 2 if the lame-duck Congress and the president can’t agree on a plan to rein in the federal deficit or buy more time to do so.

The Budget Control Act of 2011 shrinks the Pentagon budget in two phases — $487 billion through 2021 and an additional $500 billion unless action is taken to avert the across-the- board cuts known as sequestration. Non-defense “discretionary” spending, including foreign aid, would be cut by 8.2 percent.

The defense industry has said sequestration would cost tens of thousands of jobs, and Defense Secretary Leon Panetta has said it would be “devastating” to the military.

At the same time, a rising China and an intransigent Iran underscore a need to add to the Navy’s nine available aircraft carrier strike groups, said John Nagl, a research fellow at the U.S. Naval Academy in Annapolis, Maryland.

Iran, Syria

One of the highest-stakes diplomatic challenges will be convincing Iran’s Supreme Leader Ayatollah Ali Khamenei to abandon his nation’s suspected pursuit of nuclear weapons. If economic sanctions and diplomacy fail to produce results by sometime next year, the president may be forced to risk a war with Iran.

Kenneth Katzman, a Mideast specialist at the nonpartisan Congressional Research Service, said more economic sanctions are the likely next step, along with repeated pledges to use force if necessary. The president also must make clear that if Iran compromises, the sanctions that have hobbled its trade and tanked its currency will be lifted, he said.

The president also will be under growing pressure to intervene in the bloody civil war in Syria, an Iranian ally, which is destabilizing neighboring Lebanon, threatening Turkey and Jordan and attracting a new generation of radical Islamists.

Al-Qaeda’s ‘Franchise’

Syria isn’t the only battleground for the evolving terror threat. While al-Qaeda has been battered in Afghanistan and Pakistan, it has metastasized into an “amorphous movement” whose affiliates in numerous countries could “plot acts of terrorism against the U.S. homeland,” Katzman said in an interview.

Jeffrey Dressler, an analyst at the Institute for the Study of War, a Washington policy group, said extremists have increased their presence in Egypt, Libya, Algeria, Mali, Yemen and Somalia. The al-Qaeda “global franchise,” he said, “is going to pose even more significant challenges in five or 10 years.”

To slow extremism’s progress, the president will have to do more than use drone strikes and special operations forces, Dressler said. Shrinking budgets notwithstanding, the administration will need to target the poverty and official corruption that allow militant Islam to flourish, he said.

Changing Egypt

Obama faces unfamiliar terrain in the Middle East as the protest movements that swept the region continue to alter internal politics and foreign relations.

The long U.S. alliance with Egypt will be reshaped, said Jon Alterman, director of the Middle East program at the Center for Strategic and International Studies, a Washington policy group. What comes next under the Muslim Brotherhood government is critical to preserving Egypt’s peace accord with Israel and to maintaining priority access for the U.S. military through the Suez Canal.

The moribund Palestinian-Israeli peace process may be unlikely to draw much attention from the White House. If Israeli Prime Minister Benjamin Netanyahu is able to form a new government in early 2013, U.S.-Israeli ties may continue to be strained by the tension in his relationship with Obama.

In the near-term, Obama will have to manage the drawdown of U.S. combat forces from Afghanistan he’s promised by the end of 2014 without abandoning the Afghan government or letting insurgents reverse fragile gains. He probably will seek to keep 10,000 to 15,000 non-combat forces in the country to support counter-terrorism operations and train and advise Afghan forces, Nagl said.

China Challenges

Elsewhere in Asia, the president faces economic, diplomatic and strategic challenges from China, where he’ll need to engage new leaders and soothe ill feelings from the anti-China rhetoric of the presidential campaign. While China is America’s second- largest trading partner, the two nations have been embroiled since 2009 in disputes over autos, rare-earth minerals, steel, tires, chicken parts, electronic-payment services, government support for clean energy and other issues.

Trade Deficit

The U.S. goods trade deficit with China reached a record $295.4 billion last year, and the Obama administration has said the Chinese yuan is undervalued at the expense of U.S. exports. How much pressure the U.S. can exert may be limited by China’s status as the top U.S. creditor.

China had made clear “the ball is in the U.S. court” to restore a “positive and cooperative” tone, said Chris Johnson, a China specialist and former CIA analyst at the Center for Strategic and International Studies in Washington.

Across Asia, the administration needs to impress on China, Japan and others the importance of peacefully resolving island claims in the energy-rich East and South China Seas, analysts said. Obama will have to try to get them to resolve their differences “without wading into the very nasty waters of all these territorial disputes,” said Michael Kugelman, an Asia analyst at the Wilson Center.

As the euro crisis enters its fourth year, it remains an unpredictable threat to the global economy and a constraint on the U.S.’s traditional allies. Belt-tightening coupled with war fatigue after military actions in Iraq, Afghanistan and Libya means there’s scant appetite in Europe for interventions to stabilize nations such as Somalia and Mali.