But Sessions has named a US attorney to lead a review of the topics that the legislators had requested he explore.
In a letter Thursday to three leading Republicans in Congress, Sessions said the appointment of a special counsel is reserved for "extraordinary circumstances".
The Republicans had called for Sessions to appoint a second special counsel to look into the FBI's handling of aspects of the investigation into Russian meddling in the US presidential election and matters related to former secretary of state Hillary Clinton and her family's foundation.
The FBI investigated Clinton's use of a private email server during her tenure as secretary of state. The investigation did not lead to prosecution of the former first lady, which US President Donald Trump and other Republicans have denounced.
Sessions revealed in the letter that he had named US Attorney John W Huber to lead a review of issues previously raised by the lawmakers.
He said he received regular updates from Huber and would receive his recommendations after his review is complete to consider whether any matters merit a special counsel.
The current special counsel, Robert Mueller, was appointed last May to look into Russian meddling in the election in a high-profile investigation.
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