Pressure from soaring health-care and pension costs coupled with cuts in state and federal aid are undermining the improving but still shaky financial health of the nation’s cities, according to a report released Thursday.

The National League of Cities, which advocates on behalf of 1,700 member cities, said its annual survey of local finance officers reflects a slowly brightening financial picture in many cities. Still, the survey found that cities continue to suffer the effects of the recent economic downturn, as well as structural problems that are making it difficult for them to pay for core services such as public safety.

The survey found that after six straight years of decline, cities this year reported a small increase in general fund revenue — the locally generated taxes, fees and outside aid that officials have wide discretion to spend on serv­ices from public safety to parks.

Sales and income tax revenue are up, but property taxes continue to decline because they typically reflect property values as much as several years before their collections. For cities, that means that their tax revenue is still depressed by the steep drop in property values that accompanied the downturn.

Despite the problems, the report found that few cities are facing the extreme pressure that since 2011 has caused Jefferson County, Ala., Stockton and San Bernadino, Calif., and Detroit to topple into bankruptcy.

Overall, nearly three in four of the 350 city finance officers surveyed reported that their cities are better able to meet financial needs in 2013 than they were in 2012. But many also reported that they have been forced to squeeze jobs out of the budget, reduce health-care and pension benefits, raise fees and sometimes increase taxes to make ends meet.

Cities will probably have to continue doing so, particularly because of the growing burden they face from pension and health-care costs.

Adding to their woes is the uncertainty surrounding state and federal aid. Many states reduced aid to localities to get through the budget crises spawned by the recent economic downturn. Meanwhile, the ongoing federal budget crisis has already led to cuts in programs that help cities, and many finance officers expect more of the same in the foreseeable future.

“Cities’ fiscal conditions remain vulnerable to external policy shifts in the face of a gradual and tenuous economic recovery, including cuts in federal spending,” the report said.