BMP Poland inked the multi-million dollar deal with the man, named as Sam Ssimbwa, who had presented himself to the company as an agent for Uganda's defence ministry, a police spokesman said.
Ssimbwa was taken into custody Thursday, spokesman Emillian Kayima said, adding that he and unnamed co-conspirators had already pocketed 520,000 euros "as part payment for consultancy fees regarding the transaction."
Ssimbwa and his associates, who have not been detained, designed an elaborate fraud including the creation of a fake public call for tender.
Spokesman Kayima said investigators had asked BMP Poland "to provide police with evidence regarding the fraud".
A BMP representative contacted at company headquarters in Warsaw confirmed it had "contacts in Uganda" but declined to comment "until the situation is resolved".
Uganda's army refuted press reports meanwhile that the army chief was implicated in the scandal.
It also denied the military investigative branch's deputy had been transferred to Somalia in secret while investigating the case.
The army denied any such meeting took place.
"The public is hereby assured that the reports are unfounded, malicious and aimed at tainting the hard earned good image of the Uganda People's Defence Forces," spokesman Paddy Ankunda said in a statement.
"Any persons who try to break this bond will be stopped using the strong arm of the law", he added.
The purported Defence ministry documents said Uganda's military was also looking for body armour, anti-riot equipment, armoured personnel carriers and self-propelled artillery systems.
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