While Rawls himself did not offer a theory regarding the ethics of eugenics, I believe that Rawls would argue that we have a strong moral obligation to promote good births, which is the original meaning of eugenics, asserted by its founding theorist, Francis Galton. (It is an intellectual mistake to relate eugenics to the historical atrocity since Hitler himself regarded his atrocious act as the final solution to the Jewish Question, not as a method of eugenics.) Here, I first explain the morality of eugenics and then explain why Rawls has to espouse the duty to eugenics.
The morality of eugenics
The duty to eugenics (or good birth) is founded on common sense. We frown upon a pregnant woman heavily drinking or taking cigarettes. We think it is morally permissible to abort a fetus if a prenatal test reveals serious defects in the fetus. Our disapproval or permission originates from the concern for the wellbeing of the next generation. The scope of duty to eugenics, however, is unclear. Galton, due to the limit of technology of his time, suggested selective breeding as the method. Living in the era where human life can be reduced to the information of bits of 0's and 1's, and creating life can mean nothing but ingenious circuit designing (in synthetic biology), we wonder how far our duty to eugenics would extend. Negative eugenics moralists would argue that the selection against genes associated with disease and disability is morally permissible. Positive eugenics moralists, on the other hand, would permit the selection of 'superficial' genes (like height or eye color) since parents should ensure the best genes for their future children for the sake of the wellbeing of the children.
The original position and eugenics
As the questioner helpfully highlighted ("a society is to take steps at least to preserve the general level of natural abilities and to prevent the diffusion of serious defects"), Rawls clearly endorses negative eugenics morality. Rawls seems to be open to the positive eugenics morality, since the negative eugenics is a minimal requirement for him. Given the paucity of Ralws' commitment on this matter, pursuing any further on Rawls' stance on this matter is unfruitful.
What is fruitful to pursue is why the (negative) duty to eugenics matters to Rawls, when most scholars find the duty to be tangential in political or social philosophy. The reason, I maintain, is due to the conceptual defect in the original position. The original position is a place where a social contact, although hypothetical, is taking place. Behind the veil of ignorance, each is equal, rational and reasonable, and expects mutual benefits. They are rational in that they know what are genuine goods for them. They are reasonable in that they are not envious of the bundles of goods of others and able to arrive at the consensus that they can live by when the veil of ignorance is lifted.
The postulate of the original position has been widely criticized for various reasons. For our purpose, relating to eugenics, the feminist criticism is most relevant. Martha Nussbaum, for one, argued that in no society individuals are equal: individuals are fundamentally and undeniably unequal in their capability. Many depend on the care of others for a long period of time (e..g., children, chronically disabling illness, or lifetime of severe disability). These people have no representation in the original position, which envisions the contracting individual as an unattached single man. To Rawls these 'attached, care-needing' individuals are anomalies in his theory of justice, and can be represented only after the veil is lifted, through legislative and judicial means. This concession means that the just society obtained through the original position is limited in its scope of justice. There then is reason for Rawls to endorse the duty to (negative) eugenics, that all members of society be as normal (meaning, equal and independent) as possible, so as to be a member in the original position.
1. "Eugenics" in Stanford Encyclopedia of philosophy
2. "Feminist Perspectives on Disability" also in SEP