Laser-driven accelerators allow to generate ultrashort (from femto- to picoseconds) high peak dose-rate (up to tens of GGy/s) accelerated particle beams. However, the radiobiological effects of ultrashort pulsed irradiation are still poorly studied. The aim of this work was to compare the formation and elimination of γH2AX and 53BP1 foci (well known markers for DNA double-strand breaks (DSBs)) in Hela cells exposed to ultrashort pulsed electron beams generated by Advanced Research Electron Accelerator Laboratory (AREAL) accelerator (electron energy 3.6 MeV, pulse duration 450 fs, pulse repetition rates 2 or 20 Hz) and quasi-continuous radiation generated by Varian accelerator (electron energy 4 MeV) at doses of 250–1000 mGy. Additionally, a study on the dose–response relationships of changes in the number of residual γH2AX foci in HeLa and A549 cells 24 h after irradiation at doses of 500–10,000 mGy were performed. We found no statistically significant differences in γH2AX and 53BP1 foci yields at 1 h after exposure to 2 Hz ultrashort pulse vs. quasi-continuous radiations. In contrast, 20 Hz ultrashort pulse irradiation resulted in 1.27-fold higher foci yields as compared to the quasi-continuous one. After 24 h of pulse irradiation at doses of 500–10,000 mGy the number of residual γH2AX foci in Hela and A549 cells was 1.7–2.9 times higher compared to that of quasi-continuous irradiation. Overall, the obtained results suggest the slower repair rate for DSBs induced by ultrashort pulse irradiation in comparison to DSBs induced by quasi-continuous irradiation.