The high eccentricities of the known extrasolar planets remain largely unexplained .
We explore the possibility that eccentricities are excited in the outer parts of an extended planetary disk by encounters with stars passing at a few hundreds of AU .
After the encounter , eccentricity disturbances propagate inward due to secular interactions in the disks , eventually exciting the innermost planets .
We study how the inward propagation of eccentricity in planetary disks depends on the number and masses of the planets and spacing between them and on the overall surface-density distribution in the disk .
The main governing factors are the large-scale surface-density distribution and the total size of the system .
If the smeared-out surface density is approximated by a power-law \Sigma ( r ) \propto r ^ { - q } , then eccentricity disturbances propagate inward efficiently for flat density distributions with q \lesssim 1 .
If this condition is satisfied and the size of the planetary system is 50 AU or larger , the typical eccentricities excited by this mechanism by field star encounters in the solar neighborhood over 5 Gyr are in the range 0.01-0.1 .
Higher eccentricities ( > 0.1 ) may be excited in planetary systems around stars that are formed in relatively dense , long-lived open clusters .
Therefore , this mechanism may provide a natural way to excite the eccentricities of extrasolar planets .