The events recorded by ARGO-YBJ in more than five. years of data collection have been analyzed to determine the diffuse gamma-ray emission in the Galactic plane at Galactic longitudes 25 degrees < l < 100 degrees and Galactic latitudes vertical bar b vertical bar < 5 degrees. The energy range covered by this analysis, from similar to 350 GeV to similar to 2 TeV, allows the connection of the region explored by Fermi with the multi-TeV measurements carried out by Milagro. Our analysis has been focused on two selected regions of the Galactic plane, i.e., 40 degrees < l < 100 degrees and 65 degrees < l < 85 degrees (the Cygnus region), where Milagro observed an excess with respect to the predictions of current models. Great care has been taken in order to mask the most intense gamma-ray sources, including the TeV counterpart of the Cygnus cocoon recently identified by ARGO-YBJ, and to remove residual contributions. The ARGO-YBJ results do not show any excess at sub-TeV energies corresponding to the excess found by Milagro, and are consistent with the predictions of the Fermi model for the diffuse Galactic emission. From the measured energy distribution we derive spectral indices and the differential flux at 1 TeV of the diffuse gamma-ray emission in the sky regions investigated.