We report the detection of the propargyl radical (CH2CCH) in the cold dark cloud TMC-1 in the λ 3 mm wavelength band. We recently discovered this species in space toward the same source at a wavelength of λ 8 mm. In those observations, various hyperfine components of the 20,2–10,1 rotational transition, at 37.5 GHz, were detected using the Yebes 40 m telescope. Here, we used the IRAM 30 m telescope to detect ten hyperfine components of the 50,5–40,4 rotational transition, lying at 93.6 GHz. The observed frequencies differ by 0.2 MHz with respect to the predictions from available laboratory data. This difference is significant for a radio-astronomical search for CH2CCH in interstellar sources with narrow lines. We thus included the measured frequencies in a new spectroscopic analysis to provide accurate frequency predictions for the interstellar search for propargyl at millimeter wavelengths. Moreover, we recommend that future searches for CH2CCH in cold interstellar clouds be carried out at λ 3 mm rather than at λ 8 mm. The 50,5–40,4 transition is about five times more intense than the 20,2–10,1 one in TMC-1, which implies that detecting the former requires about seven times less telescope time than detecting the latter. We constrain the rotational temperature of CH2CCH in TMC-1 to 9.9 ± 1.5 K, which indicates that the rotational levels of this species are thermalized at the gas kinetic temperature. The revised value of the column density of CH2CCH (including ortho and para species) is (1.0 ± 0.2) × 1014 cm−2, and thus the CH2CCH/CH3CCH abundance ratio is revised slightly higher, approaching one. This study opens the door to future detections of CH2CCH in other cold interstellar clouds, making it possible to further investigate the role of this very abundant hydrocarbon radical in the synthesis of large organic molecules, such as aromatic rings.