Water is a key volatile that provides insights into the initial stages of planet formation. The low water abundances inferred from water observations toward low-mass protostellar objects may point to a rapid locking of water as ice by large dust grains during star and planet formation. However, little is known about the water vapor abundance in newly formed planet-forming disks. We aim to determine the water abundance in embedded Keplerian disks through spatially-resolved observations of H$_2^{18}$O lines to understand the evolution of water during star and planet formation. We present H$_2^{18}$O line observations with ALMA and NOEMA millimeter interferometers toward five young stellar objects. NOEMA observed the 3$_{1,3}$ - $2_{2,0}$ line (E$_{rm up}$ = 203.7 K) while ALMA targeted the $4_{1,4}$ - $3_{2,1}$ line (E$_{rm up}$ = 322.0 K). Water column densities are derived considering optically thin and thermalized emission. Our observations are sensitive to the emission from the known Keplerian disks around three out of the five Class I objects in the sample. No H$_2^{18}$O emission is detected toward any of our five Class I disks. We report upper limits to the integrated line intensities. The inferred water column densities in Class I disks are N < 10$^{15}$ cm$^{-2}$ on 100 au scales which include both disk and envelope. The upper limits imply a disk-averaged water abundance of $lesssim 10^{-6}$ with respect to H$_2$ for Class I objects. After taking into account the physical structure of the disk, the upper limit to the water abundance averaged over the inner warm disk with $T>$ 100 K is between 10$^{-7}$ up to 10$^{-5}$. Water vapor is not abundant in warm protostellar envelopes around Class I protostars. Upper limits to the water vapor column densities in Class I disks are at least two orders magnitude lower than values found in Class 0 disk-like structures.
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