Wells Fargo & Co. laid off about 60 employees in its mortgage division as the bank continues to reshuffle parts of its business following heightened regulatory scrutiny, according to people familiar with the matter.

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The San Francisco-based bank laid off around 40 people in recent weeks in its group that inspects the quality of mortgages, an area that has been affected by changes in the approach Wells Fargo uses to review customer files, some of the people said.

The bank also let go roughly 20 market lending managers across the country as part of broader operational changes, these people said. Those moves followed regulatory investigations related to improper customer charges in the mortgage division, the people familiar with the layoffs said.

Wells Fargo spokesman Tom Goyda said the bank "announced a small number of job reductions within our fulfillment and underwriting teams and always are evaluating our overall staffing levels."

The number of employees let go at the bank, the largest U.S. mortgage lender by volume, is small relative to total staff of 268,000 at the end of September.

Mr. Goyda said that the bank is currently working to hire more than 1,500 people for a variety of mortgage-related roles in the U.S., though that hiring doesn't reflect a net increase in head count.

The recent layoffs follow disclosures this summer by the bank that it charged some customers improper fees to extend interest-rate commitments they received from Wells Fargo on their mortgage applications.

In October, the bank said it is reaching out to around 110,000 customers who paid a total of $98 million in such fees. Wells Fargo said it expects refunds to be lower than that total because the bank "believes a substantial number of those fees were appropriately charged under its policy."

The Consumer Financial Protection Bureau and the Office of the Comptroller of the Currency have been investigating those activities. In November, the OCC sent Wells Fargo's board a letter saying the regulator is weighing a formal enforcement action against the bank related to improprieties in its auto-insurance and mortgage operations, among repeated failures to correct problems in other areas as well, The Wall Street Journal has reported. Wells Fargo asked, and received, an extension to respond to the letter, people familiar with the correspondence said.

The bank responded to the OCC in recent days, these people said. In its reply, the bank made a case for why it shouldn't get hit with a consent order, usually taken when the regulator determines that deficiencies in a bank's operations are severe or uncorrected, for example. The bank cited the work it has done over the past year to fix problems, one of these people said.

Mr. Goyda declined to acknowledge the letter or comment on the bank's response. More generally, in a late-November statement, the bank said there "is still work to be done," and that it "is dedicated to making things right, fixing the problems, and building a better bank."

The CFPB is also reviewing whether there should be fines against the bank for those mortgage problems, Reuters reported last week. That caught the attention of President Donald Trump, who tweeted that the bank, which in late 2016 was hit with a sales-practices scandal, should be subject to fines.

A spokesman said the CFPB can't comment on any pending enforcement matters. He added: "However, as a matter of principle, Acting Director [Mick] Mulvaney shares the president's firm commitment to punishing bad actors and protecting American consumers."

Wells Fargo's layoffs hit during a time of broader pressures in the mortgage market, especially as nonbank lenders continue to gain more footing. Capital One Financial Corp. said last month it is planning to layoff around 900 employees in coming months as the bank exits from its mortgage-lending and home-equity business.

Wells Fargo originated $59 billion in home loans in the third quarter of 2017 compared with $70 billion a year earlier.

Write to Emily Glazer at emily.glazer@wsj.com