Protesters are attempting to bring down the government of Prime Minister Yingluck Shinawatra and five people have been killed in clashes over the past week. The two sides reached a truce to mark the king's birthday.
The 86-year-old king is the only monarch most Thais have known and has been a father figure who has defused previous crises. His words were awaited with expectation.
The world's longest-reigning monarch, who left hospital in July after a four-year stay, looked sombre and spoke slowly as he read out his address.
He referred to people doing their duty to support each other. "All Thais should realise this point a lot and behave and perform our duties accordingly, our duty for the sake of the public, for stability, security for our nation of Thailand," the king told a gathering of the country's top leaders.
The birthday ceremony was held at the king's seaside palace in Hua Hin, 118 miles south of Bangkok.
Among those in attendance was the prime minister, the heads of the armed forces and police, top bureaucrats and the leader of the opposition. The queen, who suffered a stroke in July last year, was not seen in television pictures.