"While it's critical that we ensure every vote is counted and recorded, we believe that the current tally shows Mike Garcia is the likely victor in the May 12 special election. As such, I'd like to congratulate him," Smith said in a statement.
On Wednesday morning, Garcia was leading Smith by about 12,000 votes in a race previously considered too close to call.
Garcia, a former Navy pilot, will represent California's 25th congressional district through November.
Garcia and Smith are expected to face off again in the fall to win a full term.
In-person voting starts for special election to fill Katie Hill seat in northern LA County