Yates County Sheriff Ronald Spike said five people in the van were pronounced dead at the scene of the 12:40 p.m. crash and eight were taken to hospitals, some with "very serious" injuries. The tractor driver was also taken to a hospital. The car's driver had minor injuries but was not hospitalized.
There were 14 people in the van; the driver was not Amish, as they generally don't drive.
Among the dead was at least one married couple.
"In passing, (the car) glanced off the van and went off the highway and the van ended up going underneath the farm tractor," Spike said. The car tried to go around the tractor in a no-passing zone near where the 55-mph stretch of two-lane blacktop curves and signs recommend reducing speed to 45 mph.
"It's just a horrific tragedy," Spike said. "It really strained the EMS services and fire departments. There was a lot of hard work at the scene."
The driver of the car that tried to pass the tractor, a man from nearby Penn Yan, was being questioned late Tuesday afternoon.
No names of the dead and injured were available Tuesday afternoon. "We have yet to identify a lot of the individuals," Spike said, adding that the task was made difficult because many Amish do not carry identification. One of the survivors was able to give them some information at the scene.
Relatives were gathering at a church in Steuben County, south of the crash scene, awaiting information on the victims.
He said the victims were all adults from Steuben County. The group was visiting other farms on an excursion organized by Cornell University to learn techniques compatible with their religion. Spike said authorities initially thought the farmers were Mennonites.
New York has seen a boomlet in new Amish colonies recently, driven by affordable rural farmland and proximity to traditional population centers. A study by researchers at Elizabethtown College in Pennsylvania found the Amish have established 10 new settlements in New York since the start of 2010. Total population has grown by more than a third in the past two years, to 13,000.
The tractor was carrying a large spraying implement. At least four people were stuck in the wreckage before they were removed by emergency responders who used power cutting tools to free them. Four hours after the crash, responders were still removing pieces of the van from under the tractor and loading it on a flatbed truck.
"It took a long time to get the individuals out because the van ended up entangled and underneath the large tractor with the spray equipment on it," Spike said.
"It's probably one of the worst accidents we've had in this county that I can remember," he said.
The crash happened 43 miles southeast of Rochester and about 30 miles northeast of the spot in Steuben County where a tour bus crashed Sunday on Interstate 390, killing two people and injuring 35. It's a mostly agricultural swath of land, and the road where Tuesday's accident happened carves its way between large soybean fields.
A dispatcher said four helicopters, several fire departments and about a dozen ambulances services were called to the scene.
Karin Christensen at Strong Memorial Hospital in Rochester said four of the injured are at the hospital and another was expected.
Tim Raths contributed to this report from Washington, D.C., and Mary Esch contributed from Albany.