Rents in Adelaide continue to rise over the first quarter of the year, hitting record highs, according to the latest rental market report from Domain.

Over the quarter, weekly house rents increased by $15 to $425, while unit rents went up by $10 to $350. These are the steepest quarter and annual increases in house rents since 2009, up 3.7% and 7.6%, respectively.

"Despite rising rents, Adelaide remains the most affordable capital city for tenants," said Nicola Powell, senior research analyst at Domain.

However, it is worth noting that the gap between the house rents in Adelaide and Melbourne continues to narrow.

"If the pace of rental growth continues Adelaide could overtake Melbourne in coming months," Powell said.

The rising rents could be due to Adelaide's falling vacancy rates, which hit a multi-year low of 0.6%. Several factors could explain this.

Powell said more Australians are relocating to South Australia. This is reflected in the interstate migration numbers, which have been growing for two consecutive quarters.

Furthermore, investment activity and apartment construction have been subdued in recent years, which has limited the rental supply.

"Tenants will find less choice as the estimated pool of available rentals has shrunk by 17 per cent compared to the same time last year," Powell said.