WASHINGTON — As President Donald Trump continued his extraordinary public flogging of Attorney General Jeff Sessions, prominent figures in Congress and the conservative media began to rally around the embattled attorney general and warn Trump against firing him.

Trump kept up his criticism of his attorney general on Tuesday but ducked opportunities to call for him to resign, saying in response to a reporter’s question that “time will tell” whether Sessions remains head of the Justice Department.

The day began with a pair of tweets from the president criticizing Sessions for a “VERY weak position” on pursuing leaks and Hillary Clinton — even though Trump said after the election that he didn’t think it would be wise to pursue his political rival.

Later, speaking to reporters in the White House Rose Garden, Trump repeated that he was unhappy with Sessions’ decision to step aside from supervising the investigation into Russian efforts to sway the 2016 election and wanted to see “much tougher” treatment of leaks.

But he continued to evade questions about whether he’s planning to fire him. “I’m very disappointed with the attorney general but we’ll see what happens,” he said. “Time will tell. Time will tell.”

He also appeared to offer a new goal for Sessions to achieve to keep his job. “I want the attorney general to be much tougher on the leaks from intelligence agencies, which are leaking like rarely have they ever leaked before, at a very important level,” he said.

A growing chorus of the attorney general’s supporters said the president should keep Sessions on and stop undermining him in public.

“Jeff understands that we are a nation of laws, not men,” said Sen. Lindsey Graham, R-S.C. In a statement, Graham added that Trump’s cheering on of a Clinton investigation was “highly inappropriate” and would “run away from the long-standing American tradition of separating the law from politics regardless of party.”

In 20 years in the Senate, Sessions’ opposition to legalization of immigrants in the country without authorization and any efforts to ease criminal sentencing made him a favorite of many on the right wing of the Republican Party. He has pursued those same policies with vigor since taking over the Justice Department.

“Sessions is Trump’s good housekeeping seal of approval, in a policy sense,” said Mark Krikorian, executive director of the Washington-based Center for Immigration Studies, a group that advocates for restrictions on both legal and illegal immigration. He said anti-immigration advocates are willing to forgive Trump’s deviations from the cause because of Sessions.

“I don’t think (Trump) understands this,” Krikorian said. “Politically speaking, Trump needs Sessions a lot more than Sessions needs Trump.”

The president repeated Tuesday that he would never have appointed Sessions if he had known the attorney general would recuse himself from supervising the investigation into possible collusion between Trump’s campaign and Russian government attempts to influence the election, apparently blaming Sessions for his administration’s deepening troubles with the investigation by special counsel Robert Mueller.

Trump might have a problem getting rid of Mueller unless he finds another attorney general. The law says that only the attorney general can fire a special counsel. Because of Sessions’ recusal, the department’s No. 2 official, Deputy Attorney General Rod Rosenstein, is the acting attorney general for any matters related to the investigation.

If Trump were to nominate a new attorney general, that person would face Senate confirmation hearings that likely would be dominated by demands for assurances about Mueller’s independence.

And on Tuesday, Senate Minority Leader Chuck Schumer of New York warned that Democrats would block the alternative route of Trump appointing an attorney general during Congress’ August recess, a move he said would spark a “constitutional crisis.”

On immigration, Sessions has instructed federal prosecutors to be more aggressive about prosecuting border crossers, and he has traveled the country speaking out against so-called sanctuary cities that don’t cooperate with immigration enforcement.

Late Tuesday afternoon, he announced new rules to make sure that some policing grants go only to cities and states that agree to cooperate with agents from the Department of Homeland Security.

Washington Bureau’s Lisa Mascaro and Noah Bierman contributed.

joseph.tanfani@latimes.com