Fairfax County’s top appointed official has asked agencies to scour for cuts of as much as 5 percent over each of the next two years because of looming budget shortfalls.

County Executive Edward L. Long Jr. did not specify dollar amounts but in a memo Monday told county employees that cuts are necessary because of uncertainty over federal spending and slower-than-expected growth in Fairfax. He also warned that jobs may have to be eliminated in 2013 and 2014.

“This could mean that positions will be cut,” he said. “I know that many of the reductions will significantly impact the ability of county agencies to provide services.”

Fairfax has withstood the recession far better than many other parts of Virginia and the nation, but particular agencies have had to make cuts, including not hiring to fill vacant jobs. Still, the county has increased spending incrementally — 2 percent in general fund dollars this fiscal year as part of a county budget of more than $6.5 billion.

“Everyone would love to think we’re bouncing back from the recession,” said Sharon Bulova (D), Board of Supervisors chairman. “But that’s just not happening.”

County budget officials said the new projections are based primarily on real estate data for the past five months, a period in which home sales and prices have not been as strong as initially predicted. The county now estimates revenue — more than 60 percent of which comes from real estate taxes — to be less than anticipated.

Officials said it is too early to know the size of the shortfalls or how deep the county will have to cut, but they said Long’s call for 5 percent reductions does not necessarily mean across-the-board cuts.

Long, who noted that health insurance claims have become burdensome, issued the memo just as county agencies are about to put together budget proposals for next year. It is a long process, and supervisors will not adopt a new spending plan until April. In the meantime, Long plans to implement a multi-year budget process to “serve as a planning tool to provide county decision-makers with a broader perspective” as they work to balance budgets, his memo said.

Officials in Fairfax County, whose relatively strong economy relies heavily on federal jobs and contracts, also have to plan for “sequestration,” or billions of dollars in potential mandatory federal spending cuts early next year.

Even if the federal cuts do not materialize, it’s time for Fairfax’s leaders to “have an open, honest discussion” about which services the county should provide and which it needs to eliminate, said Supervisor Pat S. Herrity (R-Springfield). “Sequestration or not, this isn’t new,” Herrity said.