A new generation of primary national wavelength standards using an intracavity saturated absorption of 127I2 at 633 nm is reported. Relative frequency stability of (2-3) multiplied by 10-14 and a reproducibility level of about 3 parts in 1013 for 1 - 2 months have been demonstrated for the first time in the visible range. One of the key features of the new standards is a very accurate electronic servo-system based on a digital lock-in technique, which is characterized by frequency offsets much smaller than the shifts resulting from asymmetry of iodine resonances. For the standard with an 'ideal' iodine cell, a set of specially selected frequency dependencies have been measured with a low uncertainty level. This set seems to be sufficient for the on spot checking if the operation of a laser standard is normal. A new parametric tuning technique of the laser cavity has been realized, giving important improvement in the reproducibility of the standard. Results of international comparisons of the new wavelength standard performed at the Physikalisch-Technische Bundesanstalt, Germany (PTB) and the Bureau International des Poids et Mesures (BIPM) are reported. In BIPM comparisons, the frequency difference between the standards was found to be 0.7 kHz (much less than the usually reported reproducibility level of these standards). The frequency repeatability for four days of measurements was less than 1 multiplied by 10-13. In the PTB comparisons, several iodine cells were tested in the new standard, and a correlation between the spacing of the iodine resonances, gas contamination in the cell, the output frequency of the laser was established.