The Dungannon rider, who resumed road racing in 2014 after retiring in 2012, and Dan Cooper came off their bikes during the Supertwins race.
The Belfast Trust said Farquhar, 40, suffered chest and pelvic injuries.
Cooper was taken to the Causeway Hospital in Coleraine with shoulder injuries but was later discharged.
The crash, which happened at the Black Hill section of the course near Portrush, led to racing being abandoned for the night.
Farquhar was airlifted by police helicopter from the track after the accident and was taken to the Royal Victoria Hospital in Belfast.
A statement from the North West 200 organisers on Friday morning said that Farquhar remained "seriously ill in intensive care following surgery".
Belfast Trust said on Saturday that Farquhar remains "seriously ill" .
A well-known figure in motorcycling, he has won five races at the North West.
He retired from the sport in 2012 following the death of his uncle Trevor Ferguson at that year's Manx Grand Prix in the Isle of Man.
However, Farquhar resumed his road racing career in 2014, saying that his family backed his decision to return.
Thursday's earlier practice session at the meeting saw an air ambulance being deployed after a rider was hurt.
Nico Mawhinney from Castledawson crashed at the Mill Road roundabout and was transported to the Royal Victoria Hospital in Belfast, where he is said to be in a stable condition.
There has been a campaign to get an air ambulance for Northern Ireland, and a fund to help achieve this is the official charity at this North West 200.
Alastair Seeley, who won the earlier opening Supersport race to become the most successful rider in North West 200 history, was not competing in the Supertwin class where Farquhar and Cooper crashed.
"I was in the pit lane when it happened and I heard the gasp from everybody as they were watching the monitors," said Seeley.
"Our thoughts are just with the riders. I hope they have a speedy recovery."
Seeley added that all the riders "know the risks" involved in the sport.
"I always try and ride within the limit," added the Carrickfergus man.
County Tyrone's Ryan Farquhar is seriously ill after he and another rider were involved in a high-speed crash during the North West 200.