The 37-year-old man was struck by the silver BMW 1 Series on the A8011 Central Way in Cumbernauld at about 6.15pm on Thursday.
He was taken to University Hospital Monklands for treatment where he remains in a serious condition.
The 84-year-old man driving the car was also taken to hospital but Police Scotland said his injuries are not believed to be serious.
Police Constable Fraser McEwan, of the Road Policing Unit in Motherwell, said: “Our inquiries into this incident are ongoing and I would urge anyone who has information which hasn’t been passed to police yet to come forward.
“We would also be keen to speak to anyone who may have dashcam footage from the area at the time.
“Anyone with information can call 101, quoting incident 2904 of 3 June.”
Meanwhile, in a separate incident, police are also appealing for information after responding to a report of a man being struck by a car in Edinburgh on the same day.
The incident happened at about 5.25pm on Queensferry Road near the junction with Parkgrove Road.
The 33-year-old man was taken to the Edinburgh Royal Infirmary by ambulance where medical staff said his condition is stable.
The woman driving the car was not injured.
The road was closed for several hours while a collision investigation was carried out.
Police Sergeant Jennifer Forbes said: “This was a busy time of evening with lots of people and several motorists in the area.
“I would appeal to them to contact us with any information they may have as it could assist our inquiries in establishing what has happened.
“In particular, anyone with a dashcam is asked to check it as it may have captured images which could aid our investigation.”