(CNN) A US Immigration and Customs Enforcement official with knowledge of operations in several states says there has not been "any surge of arrests or activity or round-ups" in an operation to target thousands of undocumented immigrants subject to deportation orders.

While observers from 10 targeted cities have reported hearing of no significant action , the ICE official's comment is the first acknowledgment from inside the agency that the first few days of the operation have not been as large-scale as suggested

"This notion that we were going to do this massive sweep -- to be honest, there have been limited results so far," the official told CNN. "There have been no mass arrests."

The official went on to tell CNN that ICE "does arrests every day," but right now it's "business as usual. "

Last week, a senior immigration official told CNN that the five-day operation would target some 2,000 family members with court orders of removal and take place over several days in the 10 cities across the nation -- Atlanta, Baltimore, Chicago, Denver, Houston, Los Angeles, Miami, New Orleans, New York and San Francisco. The raids were expected to focus on recent arrivals to the country.

Read More