Thomas Mair gave his name as "Death to traitors, freedom for Britain", when he appeared at Westminster Magistrates' Court.
Mrs Cox, 41, was shot and stabbed in Birstall, West Yorkshire, on Thursday.
Members of her family visited the scene on Saturday to read floral tributes and thank gathered crowds for their support.
Speaking in the village's market square Kim Leadbeater, Mrs Cox's sister, described the MP as "perfect".
