In late 1940 the pope's Secretary of State, Cardinal Maglione, had heard rumours of a third anti-Jewish law in preparation and instructed Angelo Rotta, the nuncio in Budapest, on 23 October, to investigate and do whatever possible to ensure these laws were not passed. The details of the proposed law were unclear, but it would be reasonable to assume that Hungary was preparing to finalise its version of the Nuremberg laws. Rotta replied to Maglione on 2 November with news that he had been assured that any changes to the laws were for the purposes of clarification and simplification. This was a plausible response given that the Hungarian legal definition of who was and who was not a Jew rested on a mixture of racial classification and religious background.
In the end, a third anti-Jewish law was promulgated on 8 August 1941. A summary of the law can be found on this site
"Act XV of 1941 (the third Anti-Jewish Law) on “The amendment and modification of marriage law XXXI of 1894, and the related necessary racial provisions” went into effect on August 8, 1941. Using Nazi terminology in its preamble, the law applied Germany’s Nuremberg laws: everyone with at least two grandparents born into the Israelite faith was defined as a Jew. The law also forbade marriage, and legally sanctioned extramarital sexual intercourse between Jews and non-Jews, provided the male was defined a Jew and the female was not".
The bishops in the Upper House who had voted for the previous laws, voted against the legislation because it interfered in the legal status of marriages entered into by converted Jews and thus creating conflict with the authority of the Church.
Rotta transmits a sense of growing urgency in this document. Antisemitic actions are becoming more frequent. He mentioned a coal strike that was not reported in the papers, that was fuelled not by left-wing revolutionary zeal, but by anger at the Jewish owners of some of the mines.