BNP's acting Chairman Tarique Rahman handed over his passport to the British Home Office four years ago.
State Minister for Foreign Affairs M Shahriar Alam came up with the statement at a press conference at his Gulshan residence on Monday.
The state minister said Tarique's wife and daughter also handed over their passports, reports UNB.
"It indicates they do not want Bangladesh nationality," Shahriar Alam said.
The State Minister said the passports of Tarique, his wife and daughter were returned to the High Commission on June 2, 2014 through the British Home Office.
"Now, they've no travel documents to come to Bangladesh," he added.
"Had he wanted renewal of passport or extension of validity, he would have handed it over to Bangladesh High Commission in the UK,"
"But, he submitted it to the British Home Office. What does it mean? As a political person, I think, it's the refusal of nationality," he claimed.
The state minister said that "this is interesting that a convicted criminal has sent him a legal notice."
Shahriar said he is ready to face it legally as he has all the evidence regarding submission of passport.
"I welcome it. I'm ready to face it," he said, adding that it is good to know that BNP got back confidence on the law of the land.
Replying to a question whether Tarique is now a Bangladeshi citizen, Shahriar said, "I think no.
Addressing a reception hosted by the UK Awami League in honour of Prime Minister Sheikh Hasina in London on Sunday, Shahriar had said Tarique, living in London, gave up his nationality by handing over his Bangladesh passport to the UK Home Office almost four years ago.
The UK Home Office sent his passport to the Bangladesh High Commission, he added.
Earlier on Monday, Tarique sent a legal notice to Shahriar asking him to prove by 10 days his remark that he has relinquished his nationality by submitting Bangladeshi passport.
Or else, the BNP leader threatened to will file both criminal and civil cases against Shahriar Alam.
On behalf of Tarique, his lawyer Barrister Kaiser Kamal sent the notice by post to the Foreign Ministry's address.
BNP also protested the state minister's comment and challenged the Bangladesh High Commission to show Tarique Rahman's Bangladeshi passport if he submitted it.