April 22 (Reuters) - Truist Financial posted a 13.5% fall in first-quarter adjusted profit on Monday as the lender's interest income shrank on higher costs of retaining customer deposits and subdued loan demand.

U.S. banks have been grappling with increased funding costs as elevated interest rates prompt customers to move cash from banks to higher-yielding alternatives such as money-market funds for better returns.

On the other hand, higher costs of lending have discouraged borrowers, slowing loan growth, with no immediate signs of recovery as recent strong economic data delayed analysts' expectations of interest rate cuts this year.

Average loans and leases decreased to $309 billion in first quarter for Truist compared with $328 billion in the year-ago quarter.

Truist's net interest income or the difference between what it earns on loans and pays out on deposits, declined 12.5% to $3.43 billion in the first quarter. Net interest margin contracted to 2.89% versus 3.17%, a year earlier.

Adjusted net income available to common shareholders fell to $1.22 billion or 90 cents per share. That compares with $1.41 billion or $1.05 per share in the year-ago period.

The bank took a $70 million restructuring charge due to severance costs and branch closures in the quarter.

It also paid $75 million to the Federal Deposit Insurance Corporation in additional fees to cover a hole created last year by the collapse of Silicon Valley and Signature Bank.

Truist has been looking to refocus and strengthen its core banking business. In February, it agreed to sell the remaining stake in its insurance brokerage business to an investor group in a deal valued at $15.5 billion.

The lender said the sale would likely close in the second quarter. (Reporting by Manya Saini in Bengaluru; Editing by Ravi Prakash Kumar)