The stellar dynamic-based black hole mass measurements of M87 are twice thatdetermined via ionized gas kinematics; the former is closer to the estimationfrom the diameter of the gravitationally-lensed ring around the black hole.Using deeper and more comprehensive ionized gas kinematic data, we aim tobetter constrain the morphology and kinematics of the nuclear ionized gas, thusgaining insights into the reasons behind the disagreement of the measurements.We use both Narrow and Wide Field Mode integral field spectroscopic data fromthe Multi Unit Spectroscopic Explorer instrument, to model the morphology andkinematics of multiple ionized gas emission lines in the nucleus of M87. Thenew deep dataset reveals complexities in the nuclear ionized gas kinematics.Several ionized gas filaments can be traced down into the projected sphere ofinfluence. We also found evidence of a partially-filled biconical outflow. Thevelocity isophotes of the ionized gas disk are twisted and the position angleof the innermost gas disk tends toward a value perpendicular to the radio jetaxis. The complexity of the nuclear morphology and kinematics precludes themeasurement of an accurate black hole mass. The results support a 6.0 $\times10^{9}\rm M_{\odot}$ black hole in a 25\deg disk, rather than a 3.5 $\times10^{9}\rm M_{\odot}$ black hole in a 42\deg disk. The specific RIAF modelearlier proposed to reconcile the mass measurement discrepancy was also tested.In general, Keplerian disk models perform better than the RIAF model whenfitting the sub-arcsec ionized gas disk. A disk inclination close to 25\deg forthe nuclear gas disk, and the warp in the sub-arcsec ionized gas disk, help toreconcile the contradictory nature of the mass discrepancy between stellar andionized gas black hole masses, and the mis-orientation between the axes of theionized gas disk and the jet.