By Isabelle Yr Carlsson and Maggie Fick

COPENHAGEN/LONDON (Reuters) - Obesity drug-maker Novo Nordisk will spend $4.1 billion to build a U.S. facility to fill injection pens for its hugely popular weight-loss treatment Wegovy and diabetes drug Ozempic, it said on Monday.

Construction of the plant at Novo's existing main U.S. manufacturing site in Clayton, North Carolina, will be completed between 2027 and 2029, and will add 1,000 workers to the 2,500 already employed there, the Danish company said. Novo opened the site 31 years ago.

Novo told Reuters late last year it was working to increase its in-house capacity to fill the injection pens - a process known as fill-finish - at some manufacturing sites in the U.S. and Europe.

Booming demand for Wegovy in the United States and the 10 other markets where it has so far been launched has propelled Novo's shares to record highs and the company last year overtook LVMH to become Europe's most valuable listed company.

But the success has left Novo facing shortages and forced to limit the number of patients taking the once-weekly injection.

Boosting output of Wegovy has become more urgent since rival Eli Lilly launched its own obesity drug Zepbound in the U.S. in December.

Neither company can produce enough to meet demand. Some experts predict that sales for obesity treatments could reach about $150 billion annually by the early 2030s.

Since launching Wegovy in the U.S. in mid-2021, Novo has spent billions to boost production - much of it at facilities in its native Denmark but also at other sites including the one in North Carolina.

In another attempt to grow Novo's manufacturing capacity for Wegovy, Novo's controlling shareholder Novo Holdings announced in February that it would buy Catalent ( CTLT ), a large U.S.-based contract drugmaker that is a subcontractor for making Wegovy, for $16.5 billion.

Novo Holdings said that after the deal closes, it will sell three of Catalent's ( CTLT ) fill-finish sites - in Italy, Belgium, and in the U.S. - onto Novo Nordisk.

Niels Laurbjerg Nielsen, a corporate vice president at Novo who is in charge of fill-finish manufacturing at the Clayton, North Carolina facility, said he could not comment on that deal.

In an interview with Reuters, he declined to specify how many more doses would be produced there once the new fill-finish factory opened, but said the investment was part of the company's efforts to reach more patients.

The initial focus would be on producing Wegovy and Ozempic, although the manufacturing lines could produce other "future" medicines, he said, without specifying them.