Funes' first act as president was to restore diplomatic relations with Cuba, leaving the US as the last country in the Western Hemisphere with no formal ties with the Caribbean island.
A former television journalist, the 59-year-old was elected in March, becoming the country's first left-wing leader in more than 20 years.
He replaced Tony Saca, whose staunchly conservative government was one of the strongest backers of Washington in the region.
He is the first FMLN leader not have fought during the country's 1980-1992 civil war in which 75,000 people were killed, many by right-wing death squads.
Funes' elder brother Roberto was killed by police during the conflict.
After the inauguration, Clinton said the US wanted to improve relations with Latin America.
"We have to recognise that our country is not perfect either, that some of the difficulties that we had historically in forging strong and lasting relationships in our hemisphere are a result of us perhaps not listening, perhaps not paying enough attention," she told US embassy employees.