To deal with frustration among holiday shoppers hunting for its Wii game console, Nintendo Co. and retailer GameStop Corp. are launching a rain check program.

“We expect this to be a great way for consumers who desperately want a Wii to have something to put under the tree,” Nintendo of America president Reggie Fils-Aime said Friday.

The rain checks will be available at the regular Wii system price, $249.99, on Dec. 20 and 21, and will entitle buyers to get the Nintendo console before Jan. 29. Fils-Aime said “many tens of thousands of rain checks” would be available.

GameStop regularly takes deposits on hot software titles before they launch, which means it has the infrastructure to deal with the rain check program, Fils-Aime said. The company is working with other retailers, such as Wal-Mart Stores Inc. and Best Buy Co., to push out inventory from the supply chain to shelves as quickly as possible before Christmas, he added.

The Wii has been a startling success for the Japanese-based company, selling more than 6 million units in the United States since it was launched a little over a year ago. In November alone, 981,000 were sold in the U.S., according to NPD Group. That compares with 770,000 Microsoft Xbox 360s sold, and 466,000 Sony PlayStation 3s.

However, Wii sales have been constrained by supply, with units selling out minutes after going on store shelves. Nintendo has repeatedly denied rumors that it’s creating an artificial shortage by not increasing production to match demand.

“I get personal calls from people wanting to know why we don’t just manufacture more. Believe me, if it were that easy, we would,” Fils-Aime told reporters and analysts on a conference call.

“Production depends on components from a wide array of suppliers. If only one can’t increase their capacity, then we can’t increase ours,” the executive said.

After Nintendo raised production twice since April, production for the worldwide market is now at 1.8 million Wiis a month. Fils-Aime held out no hope of an imminent increase.

“We’ll keep producing at that level for quite a while,” he said. “When will we finally meet demand? There is no way to answer that question until we finally meet it.”