A tube or metal extrusion press has a stationary press frame formed by a main housing, a counter housing, a billet support carrying a billet holder, and a ram cross-member movable in the press frame between the housings. A piston-cylinder unit has a cylinder on the main housing, a piston in the cylinder, and a ram stem extending between a front end of the piston and the ram cross-member. An equalizing reservoir supplies hydraulic fluid to the piston, and a transfer passage extends between the reservoir and the cylinder rearward of the piston. A fill valve has a displacement sleeve on a rod and carries a ring piston and a fill valve body movable centrally of the cylinder in the transfer passage between an open position in which the passage has a large annular flow cross-section and a closed position in which the valve body blocks the passage.