Westminster Magistrates' Court heard charges that Christopher Lythgoe, 31, granted permission for a fellow member of banned group National Action to carry out the attack on July 1.
An unnamed 22-year-old man also appeared, charged with intending to commit acts of terrorism.
The man bought a "Gladius Machete" -- modelled on the swords used by ancient Romans -- with the intention of killing Rosie Cooper, MP for West Lancashire in northwest England.
Lythgoe, from nearby Cheshire, is charged with encouraging the 22-year-old to commit murder.
Cox, an MP from the main opposition Labour party, was shot and stabbed to death in her constituency by Thomas Mair in June 2016.
The suspects were among 11 men arrested by counter- terrorism police in raids last month.