Ruhul Kabir Rizvi criticised India over what he said was an opportunity for Sheikh Hasina to make statements.
The BNP senior joint secretary general said the move had disrespected people he described as July martyrs.
He said that allowing Hasina to engage in politics would damage relations between Bangladesh and India.
Rizvi also said that not returning a person he called a fugitive accused, despite existing law, was an affront to national sovereignty.
He alleged that Delhi had instigated the decision to allow Hasina to speak on the anniversary of her departure.
Rizvi made the remarks on 6 August after paying respects at the graves of Ziaur Rahman and Khaleda Zia in Sher-e-Bangla Nagar, Dhaka.
The visit coincided with the 37th founding anniversary of the Doctors' Association of Bangladesh.
Asked about gas, measles and dengue-related concerns, Rizvi said the government was working around the clock to address crises.
No response from Indian authorities or Sheikh Hasina was included in the evidence set.