Why wasn't King Thranduil part of the White Council?

King Thranduil seems to be a wise and powerful Elve, why isn't he part of the White Council or actively helping them during The Hobbit and afterwards?

Thranduil could easily help in Mirkwood Forrest and Laketown especially against the Necromancer and even coordinate with the Dwarves, Bard and Radagast the Brown there against Sauron, he does come across as a coward in the movies too hiding in his domain, surprising he never ended up like Grima Wormtongue and cooperated with the enemy.