The JaSaD leader died at a Dhaka hospital on Friday morning, his family said
The notice threatened civil and criminal lawsuits if the claim was not withdrawn.
The notice had been sent to State Minister Shahriar Alam on Monday afternoon by registered mail, BNP Legal Affairs Secretary Kaisar Kamal told bdnews24.com.
The lawyer also said he had sent notices to the editors of Kaler Kantho and Bangladesh Protidin that quoted the state minister.
Alam said Rahman had given up his green Bangladesh passport to the High Commission and relinquished his citizenship, according to media reports.