"She can have that opinion," Sloan, a frequent target of the Massachusetts senator and longtime Wall Street watchdog, told Jim Cramer on "Mad Money." "I think, if I'm not doing my job, as opposed to someone having an opinion about me that isn't always an informed opinion, then, of course, it would be appropriate that I'm not in this role."
Warren, who is exploring the idea of a 2020 bid for president, asked the Federal Reserve in October to maintain its growth cap on Wells Fargo until the bank fires Sloan for his implication "in the bank's repeated and egregious misconduct."
The scandal involved Wells Fargo employees opening millions of unauthorized bank accounts and has resulted in numerous penalties and millions of dollars in settlements.
Warren responded to Sloan's comments in a thread on Twitter on Monday morning:
Sloan confirmed that the Fed's growth cap will remain in place until the end of 2019 in Wells Fargo's most recent earnings report. Still, in the Friday interview, he argued that he was the best man for the CEO job.
"I think I'm the right person to run this company today," he told Cramer. "I care deeply about this company. I've been there for 31 years. I know how the company operates. I've taken responsibility. I don't think you should be criticized for taking responsibility, acknowledging mistakes you've made, which we've done, and then moving the company forward. Judge me on what I said we would do and what we've done."
Sloan, who has also been Wells Fargo's chief financial officer and led its wholesale banking division during his three-decade tenure, reiterated that he would understand calls for his resignation "if I'm not getting things done."
But, he added, "I work for our shareholders and I work on behalf of the board. They have high expectations for me and I'm exceeding those expectations."
The CEO cited some of his company's recent earnings results to support that claim: not only has Wells Fargo regained momentum in prime checking account growth — a metric that tracks consumers who bank with Wells Fargo — since it "ground to a halt" in 2016, but deposit, loan and earnings per share growth are also turning, he told Cramer.
"We made $6.1 billion in the quarter. And when you look at our earnings per share for 2018 — $4.28 — it was the highest earnings per share in 166 years," Sloan said. "You see that deposit growth [was] up year over year from a consumer standpoint, and [...] you also see loan growth. Our loan growth in the fourth quarter was the strongest that we'd seen in two years. Two years. And it was across the board."
Shares of Wells Fargo inched up in the second half of Friday's trading session after initially falling at the open. The stock has gained 8.79 percent year to date.
Sloan is one of several banking executives expected to testify before the House Financial Services committee in March, CNBC reported Thursday, citing sources familiar. J.P Morgan Chase CEO Jamie Dimon and Goldman Sachs' David Solomon are also expected to testify.
Disclosure: Cramer's charitable trust owns shares of J.P. Morgan and Goldman Sachs.