Senate Judiciary Committee Chairman Chuck Grassley appeared to send a warning to the White House on Wednesday evening: If you fire Jeff Sessions, we won't confirm you a new attorney general anytime soon.

In a message on Twitter, the Republican senator from Iowa said that "everybody in D.C." should be "warned" that the Judiciary Committee schedule was already set for the remainder of 2017, and therefore there was "no way" discussions about a new attorney general could be held.

Chuck Grassley Tweet: Everybody in D.C. Shld b warned that the agenda for the judiciary Comm is set for rest of 2017. Judges first subcabinet 2nd / AG no way

President Donald Trump has ratcheted up the pressure on his own attorney general in recent days, publicly criticizing Sessions in multiple interviews, messages and forums.

In March, Sessions said he would recuse himself from any current or future investigations related to Trump's election campaign amid backlash over his testimony about contacts with Russia. In congressional testimony, he appeared to mislead senators about his contact with Sergey Kislyak, Russian ambassador to the United States.

Critics questioned whether Sessions could be impartial in investigations related not only to Trump's campaign, but also the president's conduct more broadly, due to his former role as an advisor to Trump's campaign.

Sessions insisted that he stepped back from the Russia investigation only because of Justice Department rules related to his role in the Trump campaign, not because of his contacts with Kislyak.

Either way, Trump has been critical of that decision.

"He should not have recused himself almost immediately after he took office, and if he was going to recuse himself he should have told me to prior to taking office, and I would've quite simply picked somebody else," Trump said earlier this week.

Trump has also publicly called out his attorney general for not doing certain things:

Donald J. Trump Tweet: Attorney General Jeff Sessions has taken a VERY weak position on Hillary Clinton crimes (where are E-mails & DNC server) & Intel leakers!

—CNBC's Jacob Pramuk contributed to this report.