The present invention relates to an apparatus and a method for sealing a puncture in a tubular tissue structure or the wall of a body cavity. More specifically, the present invention is directed to an apparatus and method for sealing a puncture site in the wall of a tubular tissue structure, or in the wall of a body cavity with a stabilizer used to stabilize the material used to seal the puncture site as the material is positioned. The material is inserted into the puncture site as a ribbon or sheet on an introducer element such as a needle, a cannula, a guide wire, an introducer element adapted for dialysis, an introducer element adapted for catheterization, a trocar, or any other introducer element used to access the lumen of a tubular tissue structure or used to access a body cavity.