A B737-700 departing in moderate rain and limited visibility maneuvered at low altitude in response to a traffic advisory by the Tower and a TCAS traffic symbol at their 12 o'clock and two miles.

Narrative

Tower cleared us for takeoff with an initial heading of 360 degrees. Takeoff roll was uneventful; however; rain intensity increased to moderate right after rotation. Tower then instructed us to turn north as soon as able. First Officer acknowledged ATC's instruction. At this moment we were less than 200 AGL in limited visibility so I continued on runway heading. The Tower then called out traffic at our 12 o'clock and 2 miles. I observed the traffic on TCAS and began an immediate left turn while climbing through 300 FT. The rain intensity was moderate to heavy at this point and neither myself nor the First Officer visually acquired the traffic. Once safely clear of the conflict we returned to our assigned heading and resumed a normal climb. After the event the Tower Controller yelled at the VFR traffic and stated that it had not followed instructions and strayed into the Runway 9 departure path. This Controller did a great job in helping us avoid a collision. I estimate the closest point of approach to the traffic was about 1.5 miles as we climbed through his altitude which was about 700 AGL. Due to the extremely low altitude of the encounter (<500 FT); the TA/RA and voice annunciation functions of the TCAS were inhibited.