"We love this job, we love this department, and I plan to continue to do so as long as that is appropriate," Sessions said at a news conference announcing a cyber crime bust.
Sessions was flanked by Deputy Attorney General Rod Rosenstein and Acting FBI Director Andrew McCabe, who were both also criticized by the president in an interview with the New York Times on Wednesday.
Trump took a broad swipe at his administration's top law officers in the interview, saying he would not have appointed Sessions as attorney general if he had known he would recuse himself. The Republican president also noted Rosenstein's roots in Democratic Baltimore and that McCabe's wife took money from a leading Democrat during a political campaign.
The public lashing came after a turbulent first six months in office during which Trump fired national security adviser Michael Flynn and FBI Director James Comey, then the top official leading the probe into whether Russian meddled in the 2016 presidential election and possible ties to the Trump campaign.
Sessions recused himself in March from the Russia criminal investigation. He did so after failing to disclose at his confirmation hearing that he had held meetings last year with Russia's ambassador.
"Sessions should have never recused himself and if he was going to recuse himself, he should have told me before he took the job and I would have picked somebody else," the Times quoted Trump as saying.
Sessions was Trump's first supporter in the US Senate and helped shape his political team throughout the campaign and into the transition period after the Nov. 8 election.
He declined on Thursday to acknowledge Trump's criticism.
"I have the honor of serving as attorney general. It's something that goes beyond any thought I would have ever had for myself," Sessions said.
Similarly, Rosenstein, asked about Trump's remarks that there were very few Republicans in Baltimore, declined to comment. "I was proud to be here yesterday, I'm proud to be here today, I'll be proud to work here tomorrow," he said.
They took only a few questions before a spokesman asked if there were any questions about the department's dismantlement of AlphaBay, a "dark web" market. Seeing no hands, Sessions left as reporters shouted questions about whether he would resign.
An aide to Sessions said the recent disparaging remarks from Trump are "nothing new," given news media reports last month that the president was upset with his attorney general's decision to recuse himself from the Russia investigation.
A federal special counsel has been appointed to take over the Russia investigation, and several congressional committees are conducting their own probes. Next week, Trump's son-in-law and White House adviser, Jared Kushner, and the president's eldest son, Donald Trump Jr., are scheduled to testify before Senate panels, as well as the president's former campaign manager Paul Manafort.
The Kremlin says it did not interfere in the election, and Trump has denied any collusion between his campaign and Moscow.
In the Times interview, the president also took aim at the special counsel appointed to take over the Russia investigation, Robert Mueller, saying Mueller would be crossing a "red line" if he began investigating Trump's personal finances.
"I think that's a violation. Look, this is about Russia," Trump told the Times.
The newspaper also reported on Wednesday that Deutsche Bank AG has been in contact with federal investigators about Trump's accounts, citing two people briefed on the matter. And the bank was expecting to eventually have to provide information to Mueller, they said.
Deutsche Bank, which has loaned the Trump Organization family business millions of dollars for real-estate ventures, late last month rejected demands by Democratic lawmakers in the U.S. House of Representatives to provide details of Trump's finances, citing privacy laws.
On Capitol Hill, the Senate Judiciary Committee approved Trump's pick to replace Comey at the FBI, Christopher Wray. The full Senate was expected to take up Wray's confirmation before its August recess.