Natural gas cash prices rallied along with futures through the first three sessions of the week on supply concerns and remarkably strong cooling demand by mid-May standards.

The result: NGI’s Weekly Spot Gas National Avg. for the May 16-20 period jumped 80.5 cents to $7.920.

Supported by weather-driven demand and steady calls for U.S. exports, the June Nymex futures contract climbed through much of the week. It settled at $8.083/MMBtu on Friday, down 22.5 cents on the day but up 5.5% from the previous week’s close.

Conditions were ripe for a weekly advance in natural gas prices.

Production hovered around 94 Bcf much of the past week, according to Bloomberg’s estimates. Output remained well below the 97 Bcf peak of the past winter, amplifying concerns about adequate...