 Melchior was active in the Social Democratic Party but left this party in 1973 to co-found the Centre Democrats.He was member of the Danish Parliament 1973-75 and again 1977–2001.He was minister of traffic in the Conservative Poul Schlüter coalition government 1982–86, and Minister for Communication and Tourism in the Social Democratic Poul Nyrup Rasmussen coalition government 1993–94.