Ahmad Parchiyev, deputy chief of Federal Migration Service's Ingushetia branch, said that the Satsita camp is officially closed as of Tuesday.
"A few tents still remained there, but people are leaving," he said.
But Lorhen Gunther, a human rights activist at the camp, said that some 350-400 refugees still remain at Satsita.
Gunther, speaking by telephone from Satsita, said that migration officials on Tuesday warned the camp's residents that water and energy supplies to the camp would be cut starting on Thursday.
"While the authorities are not evicting the refugees by force, they are creating conditions for the refugees that leave them no other choice but to leave," said Usam Baisayev, the head of local office of the Russian human rights group Memorial.
The Russian government long has pushed for the refugees' return to Chechnya, trying to present it as a sign of normalisation of life in the war-ravaged region.
But many refugees fear returning to Chechnya, where fighting rages daily.
Five Russian soldiers were killed in separatist attacks over the past day, an official in the Kremlin-backed Chechen administration said on Tuesday.
Detentions and torture
In addition to the fighting, hundreds of people are rounded up daily in the Russian sweeps for suspected separatist fighters.
Chechen civilians and human rights activists say that such security operations are fraught with arbitrary detentions, beating, torture and murders.
Separatists, in turn, routinely kill local residents whom they suspect of collaboration with the federal authorities.
Russian forces re-entered
Chechnya in 1999
"When the war in Chechnya began in 1999 I was afraid for my children and myself, and now they're forcing me to return there, where normalisation is far away," a camp resident said.
In a bid to convince refugees to return to unstable Chechnya, Russian authorities have promised them good temporary accommodation and compensation payments for rebuilding their wrecked homes.
However, the temporary homes are cramped and shabby and compensation payments slow to come.
In addition to offering incentives for refugees to return, the authorities have pressured those reluctant to leave the tent camps in Ingushetia by cutting water and energy supplies.
Some former camp residents who have refused to return to Chechnya have found shelter in private housing in Ingushetia or in so-called "temporary settlements," usually derelict factories or collective farms where the buildings have been sectioned off into small cubicles.
More than 200,000 Chechen refugees lived in Ingushetia in the worst days of the latest war in Chechnya, which began in 1999. About 60,000 are still there.
Russian forces withdrew from Chechnya in 1996 following a 20-month war against separatists, leaving Chechnya de-facto independent.
They reinvaded the Caucusus republic in 1999 in an attempt to crush surging separatist sentiment. They have routinely been accused of human rights abuses.
Some estimates put the number of civilian lives lost in Chechnya at 70,000 since the first war of independence in 1994.