BRUSSELS — The United States and the European Union sought Monday to get past a rough patch in diplomatic relations to resume talks on a free trade deal that would grow what is already the world’s biggest business relationship.

Negotiators for the Obama administration and the EU say an agreement would create jobs and boost growth in the two economies, which represent almost half of global output but are still not fully recovered from recession. The trade volume in goods and services between the two economies totaled 800 billion euros, or about $1.08 trillion, last year.

The negotiations, however, are taking place against the backdrop of European pique over reported U.S. electronic espionage of EU citizens, including high-profile leaders like Germany’s Angela Merkel. The Greens in the European Parliament on Monday became the latest political group to call for the trade talks to be frozen in response.

Concerns over the talks also grew last week when a Belgian court accused the EU’s top trade official of tax fraud. European Commission spokeswoman Pia Ahrenkilde Hansen assured reporters on Monday that Karel De Gucht’s legal troubles “will not have any impact” on the talks.

But both European and U.S. officials have said the benefits of the proposed Transatlantic Trade and Investment Partnership are too great to let other issues jeopardize them. The week-long bargaining session in Brussels, which was delayed due to the U.S. government shutdown, was expected to discuss services, investment, energy and raw materials, and regulatory issues.

A deal could include a reduction in tariffs. But negotiators say the biggest boon, to business and consumers alike, could come from trimming the red tape that often makes it difficult to buy and sell across the Atlantic.

One European study has found that dealing with regulations and bureaucracy on the other side of the ocean can add 10 to 20 percent to the price of an imported item, like a car. TTIP could make it possible for a vehicle deemed safe for sale in Europe to be sold in the United States, or vice versa, without additional tests or adaptations being needed.

According to a study co-sponsored by the Atlantic Council, a Washington-based think tank, TTIP could create as many as 750,000 jobs in the United States.