Digitally controlled smoothly variable gain?
As Dave Tweed commented, a multiplying DAC (MDAC) seems the way to go. You don't mention your digital interface, frequency range or your output power requirements, so some details you'll have to work out for yourself. Analog Devices makes a wide variety of MDACs, which go all the way up to 16 bits resolution, which would give you amplitude steps of 150 microvolts. See, for instance, http://www.analog.com/static/imported-files/circuit_notes/CN0055.pdf

As to your "no calibration" requirement, I doubt if that's going to happen. Assuming you want accuracy equal to your resolution, this implies an overall gain of up to about 16, with a gain accuracy of 0.1% (10 volt max / 10 mV resolution). This in turn suggests that your external gain components will need at least 0.05% accuracy, and this will not come cheap. You'd do better to allow some adjustment. This assumes that by "calibration" you mean "adjustment". If you use lower-tolerance parts and accept the resulting inaccuracies, you'll still need a calibration cycle in the sense of putting in various input levels and measuring the resulting outputs.