Emerson's latest offer is for $225 per share, comprising $135 per share in cash and $90 per share in Emerson stock.
Rockwell's shares were up 7 percent at $202 in premarket trading but still well below the offer price. Emerson's shares were down about 2 percent at $58.50.
Milwaukee, Wisconsin-based Rockwell had rejected a $215 per share bid from Emerson in October, split in half between cash and shares. In November, Rockwell defended its strategy to operate as a standalone company.
St. Louis, Missouri-based Emerson said on Thursday it estimates about $6 billion of savings from a potential deal, equating to an additional $10 per share in value for Rockwell shareholders.
"We remain convinced there is compelling strategic, operational, and financial merit to bringing together our two companies," Emerson Chief Executive David Farr said in a statement.
"The industrial logic for this combination is clear. A combination of Emerson and Rockwell would create a leader in the $200 billion global automation market."
Rockwell was not immediately available for comment.
Emerson's strength is in process automation, helping power plants and factories in sectors such as mining and cement operate more efficiently.
Rockwell is a leader in so-called discrete automation, helping assemble component parts to manufacture items such as automobiles, household appliances, and computer systems.