WASHINGTON (Reuters) - US housing starts rose solidly in September on soaring demand for rental apartments, a sign that the housing market continues to steadily improve even as economic growth has slowed.

The Commerce Department said on Tuesday groundbreaking increased 6.5 per cent to a seasonally adjusted annual pace of 1.21 million units. It was the sixth straight month that starts were above one million units, pointing to a sustainable housing recovery.

Economists polled by Reuters had forecast groundbreaking on new homes rising to a 1.15 million-unit pace last month.

Housing is one of the few bright spots in the economy, which has been slammed by softening global demand and a strong US dollar, which have undercut exports. Efforts by businesses to reduce an inventory bulge and weak capital spending in the energy sector have also been a drag.

Economic activity has braked sharply, with third-quarter growth estimates running below a 1.5 per cent annualised rate. The economy grew at a 3.9 per cent rate in the second quarter.

Although residential construction accounts for less than 3 per cent of gross domestic product, housing has a broader impact on the economy, with rising home prices boosting household wealth and therefore supporting consumer spending.

The US dollar slipped against the euro, while prices for US Treasury debt were little changed.

Starts for multi-family projects surged 18.3 percent to a 466,000 unit pace, the highest level since June.

Multi-family construction is being driven by demand for rentals, especially by millennials, who cannot afford to buy their own homes because of higher prices and debt burdens.

Groundbreaking for single-family homes, the largest segment of the market, rose 0.3 per cent to a 740,000 unit pace. Economists say single-family building is being constrained by land and labour shortages.

Starts in the South, where most of the home construction takes place, rose 0.6 per cent to their highest level since October 2007. Groundbreaking on housing projects in the West was the highest since July 2007.

Though building permits fell 5 per cent to a 1.1 million-unit rate last month, a six-month low, the weakness is likely to be temporary amid strong confidence levels among homebuilders.

A survey on Monday showed builders' confidence rose to a near 10-year high in October, with builders upbeat about current sales conditions and expectations over the next six months.

Single-family building permits slipped 0.3 per cent last month. Multi-family building permits dropped 12.1 per cent, with permits for buildings with five units or more falling to their lowest level since December 2014.

Permits for single-family homes in the South rose to their highest level since January 2008.