Home Minister Asaduzzaman Khan Kamal said police are hunting for Bangladesh Nationalist Party (BNP) official M. A. Quayum for allegedly orchestrating the deadly shooting of Cesare Tavella in the capital late last month.
Police on Monday said four people had been arrested, three of whom they said had admitted carrying out the September 28th contract killing on orders of a so-called "big brother".
"Quayum is the big brother," Kamal told reporters on Wednesday.
Quayum, who is believed to have fled the country, is a mid-ranking BNP official and a former Dhaka councillor.
Kamal said police have "conclusive evidence" Quayum ordered the killing as part of a "conspiracy" to trigger anarchy and pile pressure on the government, although he did not elaborate.
The killing near Dhaka's diplomatic zone was the first of a series of attacks to be claimed by Islamic State (IS) and was followed days later by the gunning down of a Japanese farmer in northern Bangladesh.
A weekend bombing of the capital's main Shiite shrine, which killed one person and wounded dozens more, has further heightened the fears of minorities living in the mainly Muslim but officially secular nation.
Although that attack was also claimed by IS, the government responded by denying the extremist group was active in Bangladesh and instead rounded up dozens of Prime Minister Sheikh Hasina's opponents.
BNP secretary general Fakhrul Islam Alamgir rejected the home minister's claim, saying that it was "unacceptable and not believable".
"We've said clearly that the government should conduct proper investigations into these murders. Instead, they are using these to suppress a democratic opposition," he told AFP.
The government has consistently blamed the BNP and its main Islamist ally Jamaat-e-Islami for the unrest which has plagued Bangladesh since their refusal to take part in a January 2014 general election.
After the attack on the Shiite shrine, a former BNP lawmaker and several senior BNP and Jamaat officials were detained. Police said the arrests were related to previous unrest and not linked to Saturday's blast.
One of the four arrested over the aid worker's killing, Tamjid Ahmed Rubel, has told his family that he was forced into making a confession.
"When I went to visit him in the jail Tuesday, he told me he didn't do it but he was coerced by police to admit the false allegations," Rubel's uncle, Mainuddin Ahmed Tawhid, told AFP.
"We don't understand what is happening," Tawhid said, adding that his nephew disappeared two weeks ago.
US-based extremist monitoring group SITE defended its publication of all three IS claims after Bangladesh police cast doubt on their authenticity.
"The claims have been authenticated and found credible by SITE's rigorous verification process," the group said in a statement.