The Times, citing an internal State Department memorandum, said the threat came just weeks before Blackwater guards shot and killed 17 civilians on September 16, 2007 in Baghdad's Nisour Square.
However US embassy officials in Baghdad sided with Blackwater and the State Department investigators were ordered to leave, The Times said.
Four former Blackwater employees are currently on trial in a US court for the Nisour Square deaths.
The killing, seen as an example of the impunity enjoyed by private security firms on the US payroll in Iraq, exacerbated Iraqi resentment toward Americans.
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Blackwater guards "saw themselves as above the law," Richter wrote.
According to a State Department memo, Daniel Carroll, Blackwater's project manager in Iraq, told Richter after an argument "that he could kill me at that very moment and no one could or would do anything about it as we were in Iraq."
Richter wrote: "I took Carroll's threat seriously. We were in a combat zone where things can happen quite unexpectedly, especially when issues involve potentially negative impacts on a lucrative security contract."
Blackwater, whose license to work in Iraq was revoked by Baghdad, has since been renamed twice and after merging with a rival firm is now called Constellis Holdings.
The State Department canceled its contract with the company soon after President Barack Obama took office in January 2009.