We present Keck/LRIS follow-up spectroscopy for 13 photometric candidates of extremely metal-poor galaxies (EMPGs) selected by a machine-learning technique applied to the deep (∼26 AB mag) optical and wide-area (∼500 deg2) Subaru imaging data in the EMPRESS survey. Nine out of the 13 candidates are EMPGs with an oxygen abundance (O/H) less than ∼10% solar value (O/H)⊙, and four sources are contaminants of moderately metal-rich galaxies or no emission-line objects. Notably, two out of the nine EMPGs have extremely low stellar masses and oxygen abundances of 5 × 104-7 × 105 M⊙ and 2%-3% (O/H)⊙, respectively. With a sample of five EMPGs with (Fe/O) measurements, two (three) of which are taken from this study (the literature), we confirm that two EMPGs with the lowest (O/H) ratios of ∼2% (O/H)⊙ show high (Fe/O) ratios of ∼0.1, close to the solar abundance ratio. Comparing galaxy chemical enrichment models, we find that the two EMPGs cannot be explained by a scenario of metal-poor gas accretion/episodic star formation history due to their low (N/O) ratios. We conclude that the two EMPGs can be reproduced by the inclusion of bright hypernovae and/or hypothetical pair-instability supernovae (SNe) preferentially produced in a metal-poor environment. This conclusion implies that primordial galaxies at z ∼10 could have a high abundance of Fe that did not originate from Type Ia SNe with delays and that Fe may not serve as a cosmic clock for primordial galaxies.