The cost of renting an apartment in the Bay Area continues to soar, despite a raft of new complexes coming onto the market.

The average asking rent in the nine-county Bay Area hit $2,158 a month in the second quarter — an increase of 5.6 percent from the first quarter and 10.3 percent from the second quarter of last year, according to a survey by RealFacts.

The average rent is for market-rate apartments and town homes ranging from studios to three-bedrooms in complexes with 50 or more units.

San Francisco continued to have the highest rents — $3,229 on average, up 5.6 percent for the quarter and 9.4 percent year over year.

But Oakland had the biggest percentage gain. The average asking rent there jumped to $2,421 in the second quarter, up 10.6 percent from the first quarter and a whopping 19.1 percent year over year. “Out of the 15 properties we were tracking in Oakland, only three held rents steady. Twelve showed significant increases,” said Nick Grotjahn, a spokesman for RealFacts.

Oakland had no new apartment buildings come online during the past year, although two that are finishing up should hit the survey next quarter. But other cities have had significant increases in supply.

“People thought there was going to be a breather, especially with a lot of inventory coming online,” says Grotjahn. But the new apartments haven’t put much of a dent in rents.

In Santa Clara County, 12 large rental properties — with about 4,000 units combined — have come on the market over the past year. That’s more new inventory than in the previous four years combined, when only seven buildings with a total of 3,100 units debuted.

Yet asking rents in San Jose — home to seven new buildings over the past year — hit $2,169 in the second quarter, up 9 percent year over year. That was only slightly lower than the previous year, when rents rose 9.8 percent.

In San Francisco, nine new buildings — with a total of 2,171 units — entered the RealFacts survey over the past year. From 2009 through 2012, only seven large properties with a total of about 1,600 units came on the market in San Francisco. Yet rents in San Francisco rose 9.4 percent over the past year, compared to 7.4 percent the previous year.

“The number of new units pales in comparison to the number of new jobs in San Francisco,” says Samantha Chandler Duvall, director of acquisitions and business development with Chandler Properties. Her firm manages about 4,500 units throughout San Francisco and most new tenants are coming from outside the area, especially New York and Chicago.

In San Francisco, rents in the second quarter averaged $2,583 for a studio, $3,042 for a one bedroom/one bath unit, $4,248 for a two bed/two bath unit and $4,039 for a three bed/2 bath apartment. A three-bedroom townhome averaged $4,370.

Grotjahn said property managers have told him that demand has diminished somewhat over the past six months. Instead of getting 30 applicants for a unit, they might only be getting 20.

Bill Meyer, president of WM Properties in San Francisco, said the slowdown has been steeper than that. His firm manages apartments mainly in Pacific Heights and Nob Hill and has had five to rent in the past month. “Not only is number of applications down to one or two, traffic is also down. A year and a half ago we had 15 people show up the first night (of an open house). Now it’s down to two or three,” he says. “It’s taking us longer to get a lease signed. Instead of two or three days it is taking a couple weeks.”

But, he adds, “We are still getting them leased (before the previous tenant moves out). Our vacancy rate is still essentially zero.”

Although he has been able to increase rents by 9 or 10 percent a year, “We think the number of visitors to the open houses and time it takes to sign a lease is a leading indicator of rent softening.”

Rafael Davis, Chandler’s director of leasing, said he has seen no slowdown in applications. “You list one property, there are maybe 20 to 30 qualified tenants wanting to look at it right away.” He added that the lower the rent, “the more candidates for that space. If you list a studio for $1,850 in the Mission, you get 30 to 40 responses.”

Other Bay Area cities with big rent increases over the past year include Petaluma (18.7 percent), Belmont (16.6 percent), Milpitas (15.7 percent), and Hayward (14.9 percent.)