Laurent Dubrule/Reuters

LONDON — European leaders are hoping that President Obama’s re-election will spur progress toward a free trade agreement that could bolster economic growth on both sides of the Atlantic.

The United States and the 27-member European Union have the world’s biggest trade relationship, worth $700 billion a year in goods and services. Together, they account for almost a third of all global trade.

Officials from both sides are considering measures that would increase their trade by allowing European and American companies to operate in a single market.

By extending existing trade arrangements to further ease regulation, measures being proposed would bring down barriers that inhibit an even closer trading relationship.

“A car tested for safety in the United States could be sold in Europe without further tests, while a drug deemed safe by Brussels would not have to be approved as well by the U.S. government,” according to a Reuters report that cited examples of the benefits of a free trade agreement.

Karel De Gucht, the E.U. trade commissioner, said on Wednesday that he anticipated a green light from President Obama and European leaders to open trade negotiations early next year on an agreement that would “unlock the unparalleled potential of the transatlantic market.”

Trade is a vital issue for European politicians struggling to stimulate their stalled economies.

David Cameron, the British prime minister, singled it out in a congratulatory message to Mr. Obama in which he said, “We need to kick start the world economy and I want to see an E.U.-U.S. trade deal.”

Angela Merkel, the German chancellor, another prominent proponent of an E.U.-U.S. free trade agreement, referred in her post-election message to the President to their cooperation in overcoming the global financial and economic crisis.

Mr. Obama’s trade team has been quietly working out the details for a transatlantic free trade agreement and would be interested in pursuing it in earnest next year, according to Tyson Barker, an expert on U.S.-Europe relations, writing in the German magazine Der Spiegel this week.

Mr. Barker, the Washington-based director of transatlantic relations at the Bertelsmann Foundation, cautioned, however, that Congress could act as a wildcard in the moves toward free trade.

He said the desire of Congressional Republicans “to prevent Obama from accumulating political ‘wins’ could keep them from authorizing the administration to conduct wide-ranging treaty negotiations.”

The elected European Parliament has already given E.U. officials the go-ahead to begin the trade talks with the United States.

Its legislators say European and U.S. output could be lifted by €163 billion, or $208 billion, by 2018, if just half the existing nontariff barriers were removed.

But there are significant obstacles to a closer trading relationship in some areas, including agriculture, where the two sides disagree on the use of genetically modified crops.

Some were skeptical about whether the Obama victory made much difference to U.S. trade policy in general. Few observers of international economics or trade had expected a sharp difference between an Obama and a Romney administration, according to Alan Beattie at The Financial Times.

Mr. Beattie, writing from Washington, said it might actually have been easier for Mr. Romney to fast-track a new trade deal through Congress. “Mr. Obama will very likely have to present an almost-finished trade deal to Congress first,” he wrote.