WASHINGTON (Reuters) - U.S. President Donald Trump further stoked speculation about the fate of his attorney general, Jeff Sessions, on Wednesday by assailing him in a fresh round of tweets even as Sessions was attending meetings at the White House. On Tuesday, Trump took to Twitter to call Sessions “very weak,” prompting questions about whether Sessions, one of Trump’s earliest and most vocal supporters during his 2016 presidential campaign, would be forced out. On Wednesday, Sessions entered and left the White House  without speaking to the president and with his status unchanged, while conservative lawmakers in Congress rallied around Sessions, a former senator. A source close to Sessions said he has a “spine of steel” and plans on remaining in office until he is fired or asked to resign. Trump has kept Sessions at a distance, the source said. The two rarely speak and Sessions has been kept out of meetings.  Trump has said he is frustrated that Sessions recused himself from a federal investigation into possible collusion between Trump’s election campaign and Russia and said he would not have appointed him had he known he would do so. At a White House press briefing, spokeswoman Sarah Sanders did not address Sessions’ job security, but said that Trump and Sessions had not spoken this week. “You can be disappointed in someone but still want them to continue to do their job,” Sanders said. “The president wants the attorney general to focus on his duties as attorney general.” In a pair of morning tweets, Trump said Sessions should have named a replacement for Andrew McCabe, the acting director of the FBI. Trump has accused McCabe of having ties to his former presidential rival, Democrat Hillary Clinton. The FBI has defended McCabe, saying he did not have conflicts of interests. Trump has since nominated Christopher Wray to be the FBI director. Wray is waiting to be confirmed by the U.S. Senate.  At a news conference on Tuesday, Trump said he was “very disappointed” with Sessions. Asked whether Sessions would remain in the cabinet, Trump said, “Time will tell.”     But Republicans on Capitol Hill and conservative groups have stood by the attorney general.  Senator Lindsey Graham said Trump was acting weak by not following through and firing Sessions. “I would fire somebody I did not believe could serve me well rather than trying to humiliate them in public - which is a sign of weakness,” Graham tweeted on Wednesday.  Earlier, Graham had praised Sessions as a “rock-solid conservative” who “believes in the rule of law.” Sessions “is working to keep our streets safe, secure our borders, and enforce our immigration laws, and protect our nation,” Senator Tom Cotton said in a statement. Sessions’ hardline stance on immigration endears him to conservatives. On Tuesday, the Justice Department said it would now withhold grant money from so-called “sanctuary cities” - communities that do not cooperate with federal immigration authorities.  That move earned Sessions praise from NumbersUSA, a group that advocates limits on immigration. 