Robert Zoellick, president of the World Bank, will step down in June. (Bernat Armangue/AP)

The World Bank on Tuesday announced that President Robert Zoellick would step down when his five-year term expires in June, triggering questions about where the longtime Republican stalwart will end up next and who will replace him at the international financing institution.

A highly regarded manager, Zoellick helped steady bank morale after his predecessor, Paul Wolfowitz, resigned in 2007 amid controversy over his relationship with a bank staffer. Under Zoellick, 58, the World Bank moved in concert with the International Monetary Fund and major economic nations to battle the global financial crisis. He also pushed through a major increase in the bank’s capital resources and set up emergency support for eastern European nations whose financial systems were at risk.

Zoellick’s announcement will prompt a search by the Obama administration for a new World Bank president, traditionally chosen by the United States.

Speculation about the replacement is already well underway. Possible candidates include Secretary of State Hillary Rodham Clinton and former Obama economic adviser Lawrence H. Summers, now a professor at Harvard University, who worked for the bank in the early 1990s. Clinton has denied having an interest in the job, a position that aides said Tuesday had not changed. Summers could not be reached for comment.

Although the president is formally appointed by the bank’s member nations, a decades-old agreement — which also allows major European powers to choose the head of the IMF — gives the United States the role of naming the World Bank chief. That process came under challenge last year when European nations rallied behind then-French finance minister Christine Lagarde to take over the IMF, while developing countries argued for a more open selection process.

Similar arguments are likely to arise over Zoellick’s successor. The bank’s board is supposed to meet Thursday to decide on the procedure for selecting the next president.

But the Obama administration made clear it expected to name the next bank head, and officials said National Security Adviser Thomas E. Donilon and Chief of Staff Jack Lew would lead the search. “In the coming weeks, we plan to put forward a candidate with the experience and requisite qualities to take this institution forward,” Treasury Secretary Timothy F. Geithner said in a statement.

During his tenure, Zoellick moved the bank in new directions, supplementing its bread-and-butter development work with programs, for example, to create commodities-trading markets that allow farmers in developing nations to get more predictable prices for their crops and thus invest more in planting.

He sometimes was outspoken politically, too, criticizing the Obama administration for what he regarded as a timid approach to free trade. He pushed European leaders to resolve their credit crisis, warning of the ramifications it could have for poorer countries.

Before joining the World Bank, Zoellick had served in the George W. Bush administration as deputy secretary of state and U.S. trade representative. He had been in government service since the 1980s.

In an interview, Zoellick declined Wednesday to discuss his future, deflecting talk of a possible role in the campaign of GOP presidential front-runner Mitt Romney.

“I run an institution with 187 shareholders. I cannot be politically involved,” Zoellick said. “I will be here until June 30 and devote myself 100 percent to running the bank. I don’t have any plans yet. I can decide that when I leave.”

Still, some Republicans expect that Zoellick eventually will sign on as an adviser to Romney after his term ends in June. Romney campaign officials did not respond to questions about that possibility.

If Zoellick were to make such a move, he would join a small but prominent group already advising Romney on economic policy.

Atop that group are two well-known conservative economists: Columbia University business school dean Glenn Hubbard and Harvard University professor Greg Mankiw. Both have chaired President George W. Bush’s Council of Economic Advisers.

Like Zoellick, Hubbard and Mankiw have Ivy League pedigrees and decorated résumés that straddle public and private worlds. Both are widely respected in their field, even by liberal-leaning peers.

Hubbard, who holds a doctorate in economics from Harvard, served a stint at the Treasury Department under President George H.W. Bush and later returned to head the CEA from 2001 to 2003. He was a key architect of a series of controversial tax cuts that lowered income tax rates and reduced taxes on capital gains and other investment income. Those policies remained contentious a decade later, and President Obama agreed to extend the George W. Bush-era tax cuts in late 2010 for two years as part of a compromise with Republicans. Romney has said he wants to make those cuts permanent.

Mankiw, who excelled as a Princeton undergraduate and holds a doctorate from the Massachusetts Institute of Technology, is a longtime professor and the author of a popular textbook on the principles of economics. He maintains a widely read, often-witty economics blog and frequently contributes to the New York Times.

Like Hubbard, Mankiw also has expressed a deep skepticism for the Obama administration’s stimulus spending and its tax proposals.Other members of the Romney economic team include former Missouri senator Jim Talent, a fellow at the conservative Heritage Foundation, and former Minnesota congressman Vin Weber, who previously advised the campaign of Tim Pawlenty.

Whatever lies ahead for Zoellick, he said Tuesday he has already had an economic impact at the World Bank. He said he helped elevate it from an agency primarily involved in lending to poor nations to one that bolstered the world financial system when it was on the brink of collapse. “The bank is back in the game in a big way,” Zoellick said.

Staff writers Philip Rucker and Scott Wilson contributed to this report.