New claims for unemployment benefits fell last week, while housing starts and permits for future construction rose in May, signs that offered some hope the economy could soon pull out of its soft patch.

Initial claims for state unemployment insurance slipped 16,000 to 414,000, the Labor Department said on Thursday, suggesting the jobs market was regaining some momentum after stumbling in May.

A separate report from the Commerce Department showed housing starts rose 3.5 percent to a seasonally adjusted annual rate of 560,000 units, retracing almost half of April's steep decline.

New building permits unexpectedly rebounded 8.7 percent to a 612,000-unit pace last month, the highest level since December.

The reports were the latest to suggest some easing in the economic slowdown that started as the year began. Data this week showed modest declines in retail sales and motor vehicle production in May.

U.S. financial markets were little moved by the data, which was eclipsed by protests in Greece over the government's austerity plan.

The broader theme we have to look at is that the pace of job destruction is slowing but the pace of job creation is also a bit tepid, said Ian Pollick an economic strategist at TD Securities in Toronto.

April's housing starts were revised up to a 541,000 unit pace, which was previously reported as a 523,000 unit rate.

Economists polled by Reuters had forecast housing starts rising to a 540,000-unit rate. Compared to May last year, residential construction was down 3.4 percent.

An oversupply of previously owned houses, especially foreclosed properties which sell well below their value, is dampening new home construction. A survey on Wednesday showed sentiment among home builders at its lowest in nine months in June.

Last month, there was an increase in groundbreaking for both multi and single family homes. Starts in the West were the highest since August.

Multi-family home starts rose 2.9 percent. The increase in the construction of multi-family units reflects a growing demand for rentals as relentless declines in house prices encourage Americans to delay home purchases and even give up properties whose mortgages are far higher than their values.

Single-family home construction, which accounts for a large portion of the market, rose 3.7 percent.

Economists had expected overall building permits in May to fall to a 558,000-unit pace.

Permits were boosted by a 23.2 percent surge in the multi-family segment. Permits to build single-family homes rose 2.5 percent. New home completions climbed 0.4 percent to 544,000 units in May.

(Reporting by Lucia Mutikani and Pedro Da Costa in Washington; Additional reporting by Emily Flitter in New York; Editing by Andrea Ricci)