Mr de Guindos earned her support in part by working closely with Germany's finance minister to create a European banking union, Ms Merkel said at a news conference following a lengthy meeting with Mr Rajoy in northwestern Spain.
Ms Merkel said she backs Spanish Finance Minister Luis de Guindos to head a group that played a crucial role in the currency bloc's response to its sovereign debt crisis because he was "an excellent finance minister who guided Spain in difficult moments.
Spanish Prime Minister Mariano Rajoy said he had proposed to European leaders that Mr de Guindos succeed Jeroen Dijsselbloem, who became president of the Eurogroup in early 2013.
Spain is trying to maintain its political clout at the highest level of the European Union after a new European commissioner takes over in November from Joaquín Almunia, a Spaniard who as a vice president of the European Commission oversees competition matters.
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