In the Icelandic parliament elections of 1971, Vilmundur stood as candidate for Social Democratic Party in the Westfjords constituency. He was an active participant in the operations of the party and held a number of positions within it. He was the editor of Alþýðublaðið, the party newspaper, for a year. In the 1978 elections Vilmundur was a candidate in Reykjavík and was voted into office. From October 1979 to February 1980 he served as Minister of Justice, Religion and Education in the minority Social Democratic government. In 1982, Vilmundur left the Social Democrats and founded the Alliance of Social Democrats in 1983. The party won four seats in the elections that year.