Magnetic resonance imaging (MRI) provides excellent image contrast for various types of tissues, making it a suitable choice over other imaging modalities for various image-guided needle interventions. Furthermore, robot-assistance is maturing for surgical procedures such as percutaneous prostate and brain interventions. Although MRI-guided, robot-assisted needle interventions are approaching clinical usage, they are still typically open-loop in nature due to the lack of continuous intraoperative needle tracking. Closed-loop needle-based procedures can improve the accuracy of needle tip placement by correcting the needle trajectory during insertion. This paper proposes a system for robot-assisted, flexible asymmetric-tipped needle interventions under continuous intraoperative MRI guidance. A flexible needle's insertion depth and rotation angle are manipulated by an MRI-compatible robot in the bore of the MRI scanner during continuous multi-planar image acquisition to reach a desired target location. Experiments are performed on gelatin phantoms to assess the accuracy of needle placement into the target location. The system was able to successfully utilize live MR imaging to guide the path of the needle, and results show an average total targeting error of 2.5±0.47mm, with an average in-plane error of 2.09±0.33mm.