  We study the effect of soft gluon emission on the total cross section
predictions for the $gg\to HZ$ associated Higgs production process at the LHC.
To this end, we perform resummation of threshold corrections at the NLL
accuracy in the absolute threshold production limit and in the threshold limit
for production of a $ZH$ system with a given invariant mass. Analytical results
and numerical predictions for various possible LHC collision energies are
presented. The perturbative stability of the results is verified by including
universal NNLL effects. We find that resummation significantly reduces the
scale uncertainty of the $gg\to HZ$ contribution, which is the dominant source
of perturbative uncertainty to $ZH$ production. We use our results to evaluate
updated numbers for the total inclusive cross section of associated $pp \to ZH$
production at the LHC. The reduced scale uncertainty of the $gg\to HZ$
component translates into a decrease of the overall scale error by about a
factor of two.
