The White House maintains that President Trump has no intention of firing Jeff Sessions. However, given Trump's repeated, public attacks against his own subordinate (one of his oldest political allies), it seems likely Trump is trying to force Sessions to resign. That's one thing Jeff Sessions has reportedly refused to do.
Trump has repeatedly expressed his dissatisfaction with the direction of the Russian probe, publicly stating he never would have hired Jeff Sessions if he knew the Attorney General would recuse himself from the Russian investigation. Since, in the eyes of the law, Sessions recusing himself was the right and proper thing to do, Graham wasn't calmed at all by Trump's explanation.
Graham commented on Trump's continued actions:
This is unnerving. It’s unfair to Jeff Sessions. He’s a good man who deserves better, and some of the suggestions the president is making go way beyond what’s acceptable in a rule of law nation.