In a blender, combine the first seven ingredients; cover and process for 1-2 minutes.
On 12 metal or soaked wooden skewers, alternately thread shrimp and vegetables, leaving a small space between pieces. Place in a shallow glass container. Pour oil mixture over kabobs; cover and refrigerate for 2-3 hours.
Drain and discard marinade. Grill kabobs, uncovered, over medium heat for 6-8 minutes on each side or until shrimp turn pink and vegetables are tender. Combine butter and dill; baste over skewers. Serve with rice.