Interfax news agency quoted a spokesman for Chechnya's pro-Russian authorities as saying on Monday that "after March 1 there must not be a single tent on the territory of Ingushetia. It is the final deadline".
The Chechnya State Council spokesman added: "The main thing is that people do not live in horrible conditions in tents, where everything is rotten."
Moscow has long tried to persuade the estimated 10,000 refugees in Ingushetia to return to neighbouring Chechnya.
It says the situation is now peaceful enough in the war-devastated region, although it insists the refugees need only go home if they want.
However, rights groups and the UN have raised concerns that Russia has been forcing Chechens to return home, and say many people are too scared to go back to their homes.
According to most estimates there are around 70,000 refugees in Ingushetia, although fewer than 10,000 of these live in tents.
Russia has been fighting separatists in mainly Muslim Chechnya for nine years. It says the mountainous region on its southern border is returning to normal but its forces are subject to daily rebel attacks.
"It is not refugees' comforts that worry them. They just want rights groups and journalists to stop talking about us. For four years they have wanted the refugees to return but the problem is that the majority are scared"
Ruslan Badalev, the leader of the Chechen Committee of National Salvation
Chechen rights groups say they do not trust pro-Moscow authorities to protect their interests.
"It is not refugees' comforts that worry them. They just want rights groups and journalists to stop talking about us," said Ruslan Badalev, the leader of the Chechen Committee of National Salvation.
"For four years they have wanted the refugees to return but the problem is that the majority are scared."
Chechnya has been devastated by war for most of the last nine years.
Chechens who ruled a de facto independent Chechnya from 1996-1999 do not recognise the Moscow-backed government and have vowed to keep fighting.
Chechnya's most prominent rebel fighter vowed on Monday to continue anti-Russian attacks.
In a statement published on Monday, Shamil Basayev said: "I affirm that whatever the infidels attempt, that nothing will stop this jihad (holy struggle) which is intensified every day,"
His comments came on the same day that Russian media reported several explosions hit a government building in the Chechen capital Grozny, injuring two people.