The West Bengal CID on Thursday evening detained one person for his alleged involvement in the "murder" of Bangladesh MP Anwarul Azim Anar, an officer said.
Police suspect that the MP could have been "lured" into a New Town flat by a woman and then murdered by contract killers.
The detained person, who is a resident of an area in West Bengal close to the international border with Bangladesh, had met one of the prime accused in the murder case, the officer said.
Further investigation is underway to find out why the person had met him and what they discussed, the officer said, without divulging the identity of the detained person.
An initial probe also found out that the MP's close friend, a US citizen, had paid around Rs 5 crore to those involved in the crime, the senior police officer said.
The Awami League MP's friend owns a flat in Kolkata, and is probably in the US at present, he said.
Police also said that the flat in Kolkata's New Town area, where the Bangladesh MP was last seen entering, was rented out to his friend by its owner, an excise department employee.
"Investigation indicated that the Bangladeshi parliamentarian fell into a honey trap laid by a woman who was also close to the victim's friend. It seems, Anar was lured into the New Town flat by the woman. We suspect he was murdered soon after he went to the flat," he said.
The CID is examining the CCTV footage which showed Anar entering the flat with a man and a woman, the officer said.
"It was a well-planned murder. A huge amount of money, around Rs 5 crore, was paid by an old friend of the MP to the contract killers to execute the crime. Further investigation is underway," he said.
"In the CCTV footage, the politician was seen entering the flat with the two persons. The duo was later seen coming out and again re-entering the flat the next day but the MP was not seen again," the officer told PTI.
Police said the duo was later seen coming out of the flat with a big trolley suitcase.
Anar, who went missing in Kolkata on May 13, was found murdered and three people have been arrested, Bangladesh Home Minister Asaduzzaman Khan said on Wednesday.
The state CID, which is investigating the case, has found blood stains inside the New Town flat and also recovered several plastic bags, which they believe were used to dump the body parts.
Circumstantial evidence indicates that the MP was first strangulated and then his body was cut into several pieces, police claimed.
"We suspect that after killing Anar, the murderers mutilated the body, segregated the flesh from the bones and mixed those with turmeric powder to delay decomposition.
"Then the body parts were probably put inside plastic bags as well as in the trolley bag and scattered at different locations. We also suspect that some parts were kept in a refrigerator and we have collected samples," the officer said, adding search for the body parts was underway.
Messages were also sent from his mobile phone to a few of his contacts asking them "not to contact him as he was travelling to Delhi".
"It seems these messages were sent from the MP's mobile phone to confuse his family members and friends and prevent them from launching a search for him... there is a possibility that these messages were sent after his murder," he said.
The search for the missing MP, who reportedly arrived in Kolkata on May 12 to undergo medical treatment, began after Gopal Biswas, a resident of Baranagar in north Kolkata and an acquaintance of the Bangladeshi politician, filed a complaint with the local police on May 18.
Anar had stayed at Biswas's house upon arrival.
In his complaint, Biswas stated that Anar left his Baranagar residence for a doctor's appointment in the afternoon of May 13, while stating that he would be back home for dinner.
Biswas claimed that the Bangladesh MP went incommunicado since May 17, which prompted him to file a missing complaint a day later.