Stock futures add to gains after CPI, housing starts

U.S. stock-index futures furthered their advance on Tuesday after economic reports offered a benign view on inflation and cast a better-than-anticipated light on the housing market.

"Today's report should remind investors that broad inflation measures are not skyrocketing higher, leaving some room for the Fed as it plots its exit course," Dan Greenhaus, chief strategist at BTIG, wrote in emailed comments.

Up 47 points ahead of the data, futures for the Dow Jones Industrial Average were up 63 points in the wake of the numbers, which had the consumer price index increasing 0.1 percent in July, in line with expectations and indicating that inflation remains muted even as the economy improves.

Read MoreConsumer prices post slim gain; food costs offset by energy

Separately, home construction rose 15.7 percent last month from June.

"The housing market appears to be re-accelerating," noted Greenhaus.

Read MoreHousing starts, permits rise in July

Home Depot reported better-than-expected quarterly earnings and revenue early Tuesday, as the home-improvement retailer rebounded from a harsh winter.

Read MoreSevere winter givesway to hot spring for Home Depot

Outside the U.S., shares of Anglo-Australian mining giant BHP Billiton fell after it said it missed earnings expectations and planned to spin off the most profitable part of its business.

Read MoreBHP Billiton spins off assets, shares fall

On Monday, the Nasdaq Composite hit a 14-year high as geopolitical worries abated.

There were also positive signs from Eastern Europe. Russia said the dispute over its "humanitarian convoy" to Ukraine had been resolved and a Ukrainian official said "moderate progress" had been made after five hours of talks.

—By CNBC's Katy Barnato