A packoff assembly for sealing the annulus between the outside surface of a tubing hanger and the internal bore of a subsea wellhead includes a packoff sleeve insertable in the annulus and a seal assembly on its lower end. A release sleeve is disposed around the upper end of the packoff sleeve and is axially movable with respect thereto. An internal shoulder on the packoff sleeve receives a lock ring on the tubing hanger when the seal assembly is set to lock the packoff assembly to the tubing hanger. Circumferentially spaced apart dogs on the packoff sleeve and radially slidable on the shoulder are forced inwardly by the release sleeve when it is pulled up to retract the lock ring from the shoulder and release the packoff assembly from the tubing hanger. A running tool for running the tubing hanger and packoff assembly into the well and setting the packoff includes telescoping upper and lower body members. A surrounding sleeve is disposed around the lower body member and includes a piston surface for actuating the surrounding sleeve downwardly to set the seal assembly. Releasable latches are carried between the surrounding sleeve and the lower body member for attaching to the packoff assembly and tubing hanger. A hydraulic indicator detects sufficient downward movement of the upper body member to set the seal assembly. Emergency release a shuttle valve connected to a line in the hydraulic system to release the running tool from the tubing hanger in the event of hydraulic system failure.