The board has said it will review the $25-a-share offer, but continues to disagree with ValueAct's analysis of Acxiom's business.
In July, Acxiom rejected a $23-a-share offer from ValueAct and suggested ValueAct's criticism of Acxiom's management was linked to its managing partner's failure to get a seat on the board.
Jeffrey Ubben, the managing partner in question, continued his criticism in a letter to the Acxiom board outlining the new offer.
"The second-quarter results reported on October 19 further confirm our belief that assets are being poorly deployed, opportunities missed and that shareholder value is being eroded by current management," he wrote.
Charles D Morgan, Acxiom company leader, said: "We believe the results of this last quarter and the continuing progress we are making are evidence that we are moving in the right long-term direction."
The company made second-quarter profits of $12.4m (£6.98m), down 58% year-on-year from $29.8m. Profits were reduced by charges of $15.8m, including restructuring costs of $13m.
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