Jan 23 (Reuters) - Logitech International forecast a smaller decline in its annual sales and reported a slightly lower third-quarter revenue on Tuesday, in the computer peripheral maker's first set of results under newly appointed CEO Hanneke Faber.

Sales fell to $1.26 billion in the quarter to Dec. 31, from $1.27 billion a year earlier, as the maker of computer mice, keyboards and webcams continued to navigate a downturn in consumer and business spending as well as high comparables.

The company now expects an annual sales decline of 6%-7% to $4.2 billion-$4.25 billion. It previously forecast full-year sales decline of 9%-12%.

It forecast the non-GAAP operating income to grow by 4%-12%, and come in at $610 million-$660 million. The company had previously expected annual non-GAAP operating income in the range of $525 - $575 million.

Logitech has been dealing with customers wrestling with high inflation, and uncertainty among businesses unsure about future economic development and how to equip their offices as they move to hybrid working models. The company, based in Lausanne, Switzerland and Newark, California, said its non-GAAP operating income rose to $248 million during the period, traditionally the most important quarter of its year.

"Our teams executed well, continuing our long record of exceptional product innovation... But we will not be satisfied until we return to top line growth," Faber said in a statement.

Faber, the former head of Unilever's nutrition business, joined Logitech on Dec. 1, replacing long-standing CEO Bracken Darrell, who left to join sneaker and clothing company VF Corp last year.

(Reporting by John Revill and Disha Mishra in Bengaluru; Editing by Savio D'Souza and Rashmi Aich)