More than 3,000 other people returned from neighbouring Kenya and Ethiopia as well as from Yemen and Saudi Arabia, he said.
Hundreds of thousands of people who fled the city live in settlements along a 30km stretch of road to the west of Mogadishu. They lack tents, sanitary facilities and regular food.
Many people return to the capital because they hear conditions have improved, Redmond said.
There have been hopes that a new government voted in earlier this year will bring some measure of stability to Somalia, which has not had an effective central government since 1991.
Sharif Ahmed, the new president, was previously the leader of the Islamic courts union that brought some security when it controlled Mogadishu and the south of the country in late 2006.
However, the violence continues as armed opposition groups have declared Ahmed a traitor forcing many people to leave the country. Since January, nearly 30,000 Somalis have fled to Kenya and Ethiopia.
The worst drought in 30 years has also displaced about 10,000 within the country.
The UNHCR assists more than 460,000 Somali refugees in nearby countries, in addition to co-ordinating protection and shelter activities for the 1.3 million displaced in Somalia.