From June 2014 to February 2017, the Fermi LAT detected 46 gamma-ray bursts (GRBs) with photon energies above 20 MeV, and the trigger coordinates of seven of them were within the FoV of New-Tupi detector located in the central region of the South Atlantic Anomaly (SAA).We show in this paper that two of these seven GRBs have a probable GeV counterpart observed at ground level by New-Tupi detector. The first is GRB 160609A, a short duration GRB with a bright emission of photons over a broad energy range extending up to GeV energies. The second is GRB 160625B, a very long duration GRB, for which the Fermi LAT detected more than 300 photons with energies above 100 MeV in the ∼1 ks interval after the GBM trigger. In the first case, the signal at New-Tupi has a nominal significance of 3.5σ in the counting rate time profiles, within the T90(=5.6 s) duration on Fermi GBM. However, the effective significance is only 3.0σ. In the second case, New-Tupi detector registered at least two excess (peaks) with a nominal statistical significance of 4.8σ and 5.0σ at 438 s and 558 s after the trigger. The first is within the T90(=460 s) on Fermi GBM. Even so, the effective significance is only ∼2.0σ. In addition, from a Monte Carlo analysis, we show that the expected signal-to-noise ratio is compatible with the observation of GRB 160709A, only if the differential index of the GRB energy spectrum be equal or higher than −2.2 (a non-steep spectrum).