We introduce an algorithm for declustering earthquake catalogs based on the nearest‐neighbor analysis of seismicity. The algorithm discriminates between background and clustered events by random thinning that removes events according to a space‐varying threshold. The threshold is estimated using randomized‐reshuffled catalogs that are stationary, have independent space and time components, and preserve the space distribution of the original catalog. Analysis of catalog produced by the Epidemic Type Aftershock Sequence model demonstrates that the algorithm correctly classifies over 80% of background and clustered events, correctly reconstructs the stationary and space‐dependent background intensity, and shows high stability with respect to random realizations (over 75% of events have the same estimated type in over 90% of random realizations). The declustering algorithm is applied to the global Northern California Earthquake Data Center catalog with magnitudes m ≥ 4 during 2000–2015; a Southern California catalog with m ≥ 2.5, 3.5 during 1981–2017; an area around the 1992 Landers rupture zone with m ≥ 0.0 during 1981–2015; and the Parkfield segment of San Andreas fault with m ≥ 1.0 during 1984–2014. The null hypotheses of stationarity and space‐time independence are not rejected by several tests applied to the estimated background events of the global and Southern California catalogs with magnitude ranges Δm < 4. However, both hypotheses are rejected for catalogs with larger range of magnitudes Δm > 4. The deviations from the nulls are mainly due to local temporal fluctuations of seismicity and activity switching among subregions; they can be traced back to the original catalogs and represent genuine features of background seismicity. Key Points A new declustering method is proposed based on nearest‐neighbor analysis of earthquakes in time‐space‐magnitude domain Declustering the examined catalogs with magnitude range Δm< 4 leads to a stationary field with independent space‐time components Declustering data with Δm> 4 reveal nonstationary patterns attributed to the original catalog rather than the method