A search for periodic gravitational-wave signals from isolated neutron stars in the NAUTILUS detector data is presented. We have analyzed half a year of data over the frequency band < 922.2; 923.2 > Hz, the spindown range <-1.463 x 10(-8); 0 > Hz/s and over the entire sky. We have divided the data into two day stretches and we have analyzed each stretch coherently using matched filtering. We have imposed a low threshold for the optimal detection statistic to obtain a set of candidates that are further examined for coincidences among various data stretches. For some candidates we have also investigated the change of the signal-to-noise ratio when we increase the observation time from 2 to 4 days. Our analysis has not revealed any gravitational-wave signals. Therefore we have imposed upper limits on the dimensionless gravitational-wave amplitude over the parameter space that we have searched. Depending on frequency, our upper limit ranges from 3.4 x 10(-23) to 1.3 x 10(-22). We have attempted a statistical verification of the hypotheses leading to our conclusions. We estimate that our upper limit is accurate to within 18%.