We have searched for molecular gas towards the nucleus of four galaxie
s known to harbor a water vapor megamaser. CO(1 --> 0) emission of NGC
2639 and NGC 5506 was strong enough to allow us to map their inner re
gions. Weak emission from Mkn 1210 was detected and Mkn 1 was not dete
cted at all. We report the tentative detection of the CO(2 --> 1) line
in NGC 5506. After this work, 12 of the 18 known galaxies harboring a
water vapor megamaser have been observed in CO.The molecular gas cont
ent in the inner regions of water megamaser galaxies ranges from 5 x 1
0(7) to 6 x 10(9) M-.. The circumnuclear molecular gas surface density
also extends over nearly two orders of magnitude. The maser luminosit
y is correlated neither with the total amount of molecular gas found i
n the inner few kpc of these galaxies nor with global properties of th
e molecular gas such as surface density or filling factor; it is also
independent of the infrared and optical luminosities. The only signifi
cant correlation we have found involves the maser luminosity and the l
ow frequency radio continuum flux density. We conclude that the maser
activity is intrinsically related to the energy of the active galactic
nucleus whereas the intensity and even the presence of a water megama
ser is independent of the molecular gas global properties such as the
molecular gas content and surface density in the inner galactic region
s. We have also found a possible anticorrelation between the molecular
gas surface density and the rate of the megamaser variations. A highe
r molecular gas abundance in the inner region could lead to higher mas
er variability because of larger nuclear flux variations due to the mo
re variable gas infall, and/or because of more frequent interactions o
f the pumping agent with molecular gas condensations.