Lebanese Prime Minister Najib Mikati resigned last week. He said he was stepping down over concerns about upcoming elections and after the failure to get an extension for the tenure of a top police official.
Hague said he was concerned about Lebanon given the threat of spillover from the Syrian civil war.
"As I saw for myself last month, the crisis in Syria presents Lebanon with mounting challenges," he said in a statement.
Hague met in February with Lebanese President Michel Suleiman. He said the British government would help the Lebanese armed forces train more than 2,000 troops in the coming year.
The Lebanese military last weekend ended a campaign meant to halt border clashes between supporters and opponents of Syrian President Bashar Assad. The Daily Star newspaper in Lebanon reports more than a dozen people were killed in the clashes.
U.N. Secretary-General Ban Ki-moon called for widespread support for Suleiman during a "challenging time for the region."