BRUSSELS—The European Union and the United States announced yesterday that they have agreed to pursue talks aimed at achieving an overarching trans-Atlantic free trade deal. The 27-country EU said such an agreement, first announced in Tuesday’s State of the Union address by President Barack Obama, would be the biggest bilateral trade deal ever negotiated. Any agreement could boost the EU’s economic output by 0.5 per cent—a highly desirable outcome when the EU and the US are struggling with slow growth, high unemployment and high levels of debt. “Both of us need growth,” said Jose Manuel Barroso, president of the European Commission, the EU’s executive arm, yesterday. “And both of us have budgetary problems.” Trade between the United States and the European Union is already huge, reaching €2 billion ($2.69 billion) a day, EU Trade Commissioner Karel De Gucht said.