May 3 (Reuters) - Estee Lauder Cos Inc cut its full-year profit forecast on Tuesday as fresh COVID-19 curbs in China and the suspension of operations in Russia following the invasion of Ukraine dent the cosmetics maker's sales.

Estee's shares fell as much as 12.7%, but recovered some of those losses after company executives announced further price increases in July to offset surging costs.

The restrictions in China, a major growth market for global luxury goods makers, put the brakes on a recovery in demand for cosmetics from a pandemic-induced slump, leading the Clinique skincare maker to miss third-quarter sales estimates.

Estee's Asia-Pacific sales fell for the first time in nearly two years as the restraints in China also limited its capacity to ship orders from distribution facilities.

In contrast, French rival L'Oreal beat sales estimates last month as strong demand in Europe and North America helped counter some impact from lockdowns in China.

China generates about 36% of Estee's sales, compared to about 20% for L'Oreal, according to Jefferies analysts.

The brokerage said Estee's forecast for weaker China sales in the fourth quarter did not bode well for L'Oreal, even with its smaller exposure to the market.

Still, Estee expects to bounce back from the China slowdown, saying demand for high-end cosmetics was showing no sign of petering out even with inflation running hot and fears of an economic downturn.

"Everywhere the high luxury part (of the business) is doing better in growth than any other parts. This doesn't suggest consumers are worried by the economy," Estee Chief Executive Officer Fabrizio Freda said.

Full-year net sales are projected to rise 7% to 9%, down from a prior forecast of a 13%-16% increase.

Estee estimates adjusted annual profit between $7.05 and $7.15 per share, compared with its prior outlook of $7.43 to $7.58.

Estee's shares were last down 5% at $247.73.

(Reporting by Ananya Mariam Rajesh in Bengaluru; Editing by Shinjini Ganguli and Sriraj Kalluvila)