A suture applying device comprises a shaft which carries a pair of needles near its distal end. The needles are joined by a length of suture, and the shaft is used to both introduce the needles into a lumen of a body structure and to push the needles back through tissue on either side of the puncture site. After the needles have passed through the tissue, they are captured on the shaft and drawn outward through the tract, leaving a loop of suture behind to close the puncture site near the body lumen. The suture can then be tied and the knot pushed back through the tract to complete the closure. Alternatively, a locking fastener formed of a resorbable material can be placed into the penetration over the sutures and the sutures tied over the fastener.