Tuesday's convoy to Ingushetia comprised 34 trucks carrying more than 240 tons of food, bedding, clothes and hygiene items.
In addition to convoys to Ingushetia, which now total 19, two have been sent to Dagestan and one to North Ossetia from the UNHCR operational base in Stavropol, southern Russia, it added.
UNHCR has been providing relief for tens of thousands of internally displaced people (IDPs) who have fled Chechnya since the outbreak of hostilities in the region in August, the agency said.
Official figures place the number of displaced people who have fled Chechnya to neighbouring Ingushetia at 254,000, it added. But more than 50,000 of these had now gone back to Chechnya or to other parts of Russia.
Another 28,000 displaced were reported to be in Dagestan, while an unknown number remained in Chechnya itself.
Estimates of the number of civilians still in the Chechen capital, Grozny, range from 10,000 to 50,000, UNHCR said, adding that many of them may now be trapped in the city and unable to leave.