A suture-applying device comprises a guide body having a needle guide at its distal end. Needles are reciprocatably carried on a shaft so that they may be advanced through the needle guide and tissue into the guide body. The suturing device is used by placing the needle guide within a vascular puncture. A contact surface is provided on the guide body, and the needle guide is configured so that the vascular wall surrounding the puncture is fully exposed to the needles passing therethrough. The suturing device may be combined with a predilator to form a system for suturing vascular punctures.