  We report the results of a search for a light pseudoscalar particle $a$ that
couples to electrons and decays to $e^+e^-$ performed using the high-energy
CERN SPS H4 electron beam. If such pseudoscalar with a mass $\simeq 17$ MeV
exists, it could explain the ATOMKI anomaly. We used the NA64 data samples
collected in the "visible mode" configuration with total statistics
corresponding to $8.4\times 10^{10}$ electrons on target (EOT) in 2017 and
2018. In order to increase sensitivity to small coupling parameter $\epsilon$
we used also the data collected in 2016-2018 in the "invisible mode"
configuration of NA64 with a total statistics corresponding to $2.84\times
10^{11}$ EOT. A thorough analysis of both these data samples in the sense of
background and efficiency estimations was already performed and reported in our
previous papers devoted to the search for light vector particles and axion-like
particles (ALP). In this work we recalculate the signal yields, which are
different due to different cross section and life time of a pseudoscalar
particle $a$, and perform a new statistical analysis. As a result, the region
of the two dimensional parameter space $m_a - \epsilon$ in the mass range from
1 to 17.1 MeV is excluded. At the mass of the ATOMKI anomaly the values of
$\epsilon$ in the range $2.1 \times 10^{-4} < \epsilon < 3.2 \times 10^{-4}$
are excluded.
