Just over three weeks after the iPhone X launched, availability at Apple's retail stores is steadily improving around the world.

Apple's in-store availability tool reveals that the iPhone X is available for walk-in customers to purchase today in several major cities in the United States, including Chicago, Los Angeles, Philadelphia, Phoenix, San Francisco, although supplies vary by exact carrier, storage, and color.

Apple analyst Gene Munster, in a research note with Loup Ventures, said iPhone X availability jumped to 16 percent over the past seven days, compared to just two percent in the week prior. The data is based on daily monitoring of roughly 50 percent of Apple's stores in the United States.

Likewise, in Canada, select iPhone X configurations are available today at Apple stores in major metropolitan areas such as Calgary, Edmonton, Halifax, Montréal, Ottawa, Québec City, Toronto, and Vancouver.

A spot check of iStockNow.com revealed limited iPhone X availability for same-day pickup at Apple stores in Australia and Turkey as well, but supplies fluctuate throughout the day. Many stores receive new stock around 6 a.m. local time each day.

Apple's supply chain has addressed issues with iPhone X production, according to KGI Securities analyst Ming-Chi Kuo, so in-store inventories should continue to increase. Likewise, iPhone X orders placed on Apple.com are now estimated to ship in just 1-2 weeks, down from 5-6 weeks on launch day.

We still recommend calling your local Apple store ahead of time to confirm iPhone X availability, as supplies continue to sell out rather quickly.