The president's office has denied any involvement in the killing of Rosenberg, who was shot dead on Sunday while riding his bicycle in Guatemala City.
Amilcar Velasquez Zarate, the attorney-general, told the AFP news agency that he was handing the Rosenberg case over to the UN-supported International Commission against Impunity in Guatemala (CICIG) to guarantee its independence.
"We have no interest in hiding anything, or anyone," he said on Wednesday.
"We want to get to the bottom of this investigation."
Colom won support from the Organisation of American States (OAS), based in Washington, which passed a resolution on Wednesday approving support for his administration "in its obligation to preserve the institutions of democracy and the rule of law".
In the video, distributed on Monday, Rosenberg says: "If you are watching this message, it is because I was assassinated by President Alvaro Colom with help from Gustavo Alejos [the president's private secretary]."
Rosenberg says on the video that officials might want to kill him since he represented a businessman allegedly killed because he had refused to engage in acts of corruption that Colom purportedly invited him to participate in.
Khalil Musa, a leading Guatemalan businessman, was shot dead on April 15 in Guatemala, along with his daughter.
Audio recordings of Rosenberg's tape was distributed to local media at Rosenberg's funeral, Juan Luis Font, the director of El Periodico newspaper, said.
Video of the statement was later posted on the YouTube website.