The accident happened when the girls were digging soil for use at home, Sub-Divisional Officer Sanjay Kumar Nirala said.
While Neelam (8) and Nanhki (9) were buried alive, another unidentified girl was critically injured, he said.
The bodies have been sent for post-mortem and the injured has been admitted to Sadar Hospital where she is battling for life, the SDO said.