If there is still a gap between the opposing ends of the ring this is not a problem as it will be filled with the laser. If the ring was being soldered this gap would have to be closed.
With a small beam setting and the voltage set to 300V, take your first shots at the ring. These will deeply penetrate the metal and stitch the two sides of the ring together. Turn the ring all the way around as subsequent shots are fired, welding the two ends together and leaving a welded trough.
Once the ring is welded together, some additional wire is needed to fill the trough that the initial weld left behind. This is done by melting small amounts of 0.2 mm round wire, of the same platinum alloy as the ring, into the groove.
Widen the beam to flatten the extra molten metal along the groove. Do this by overlapping the laser shots to create flat metal puddles along the surface.
During the welding of the inside seam, the edge of the ring, which is quite thin, may begin to melt inwards as the laser follows its contour. If this happens, add more of the 0.2 mm wire to that edge to straighten out the line. You can use the same laser settings.