Story highlights Luther Strange, who currently holds Sessions' vacant seat, says he will run

State lawmaker who sought to impeach former Gov. Bentley also announces bid

(CNN) The race to replace Jeff Sessions in the US Senate is heating up.

Alabama Gov. Kay Ivey has set dates for a special election to fill the seat left vacant when Sessions became US attorney general.

"I promised to steady our ship of state," Ivey said in a statement Tuesday. "This means following the law, which clearly states the people should vote for a replacement US Senator as soon as possible."

The primary is scheduled for August 15, followed by a run-off on September 26 and the general election on December 12.

Currently, former Alabama Attorney General Luther Strange holds Sessions' vacant seat. But Alabama law calls for a governor to call a special election to replace a senator -- a law that former Gov. Robert Bentley ignored when he appointed Strange in February.