They also talked about "how these allegations will continue to be pursued".
Barr, in a letter to Trump, said he would leave his post on December 23.
The news came just moments after Joe Biden officially surpassed 270 electoral votes needed to clinch the White House after California, which has 55 Electoral College votes, the most of any state, put the former president over the top on Monday evening.
Trump has alleged widespread election fraud without evidence, while Biden has proceeded to plan his administration, appointing senior advisers and making cabinet picks despite the president's efforts to undermine his legitimacy.
In February, Barr's reversal of a sentencing recommendation for Trump ally and self-described "dirty trickster" Roger Stone, who had been convicted on witness tampering and obstruction of justice charges in Mueller's investigation, prompted four career prosecutors to quit the case - with one resigning from the department altogether.
Speaking just weeks ago about combating anti-Semitism, Jeffrey Adam Rosen, the deputy attorney general, quoted Rabbi Tarfon: "It is not incumbent on you to complete the work, but neither can you desist from doing it".
Barr went on Monday to the White House, where Trump said he submitted his letter of resignation.
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The president had been increasingly critical about a lack of arrests, and Barr was said to have privately told people that he was frustrated by Trump's public pronouncements about the case.
Trump hoped a Justice Department investigation into the allegedly political roots of the Russian Federation probe would produce a bombshell report before Election Day, giving him a much needed boost against Biden. Barr publicized his summary of Mueller's report before releasing the report itself, which had the effect of oversimplifying Mueller's findings, at least in the minds of Mueller and his deputies. "And the DHS and DOJ have looked into that, and so far, we haven't seen anything to substantiate that", Mr Barr told the Associated Press, also referring to the Department of Homeland Security.
Trump said Rosen was an "outstanding person".
Barr, in fact, enjoys a following among grassroots conservatives akin to that of past Attorneys General John Ashcroft, a staunch conservative who served under George W. Bush, and A. Mitchell Palmer, Woodrow Wilson's attorney general, famed for the "Palmer Raids" to capture Bolshevik anarchists from 1919-20.
Trump was sanguine at the time, saying he retained full confidence in Barr, but acknowledging, "I do make his job harder".
Recently, the attorney general has become something of a pariah on the right for defying Mr Trump's claims of election fraud.
In his resignation letter, Barr said he was greatly honored to have served in the Trump administration.
Trump and his Republican allies have nagged Barr to investigate the younger Biden.