Anna Kendrick Seems to Shade Blake Lively at South by Southwest Premiere of Film

Anna Kendrick doesn't seem too enthusiastic about her costar Blake Lively ... 'cause while Blake said working with Anna was "the best," Anna's response came off much more lukewarm.

The two stars pulled up to the popular film and music festival South by Southwest Friday to promote their new movie "Another Simple Favor" -- the sequel to the hit 2018 flick "A Simple Favor."

Fans and reporters lined the street to get selfies and autographs ... and, while Blake had nothing but compliments for her costar, Anna didn't have the same for Blake.

When asked what it was like working with the former "Gossip Girl" actress Anna responds "Oh, you know ... " before straight-up walking away -- basically blowing off the question entirely.

It certainly seems like Anna's following the advice every little kid gets from their parents -- if you don't have anything nice to say, don't say anything at all.

Worth noting, however ... the two were definitely talking together earlier in the day for press interviews.

Rumors about a feud between the two stars have swirled for years ... though sources with direct knowledge told us there wasn't any truth to them. We've reached out to Blake and Anna's teams for further clarification on the comment.

Of course, Blake's interaction with all her famous friends -- including longtime pal Taylor Swift -- have been under a microscope since her legal battle with Justin Baldoni began at the end of December.

Lively's claimed a smear campaign orchestrated by Baldoni's team was meant to take her down ... though Baldoni's team fired back and claimed Blake's just trying to find a scapegoat since her own image took a hit during the press tour for "It Ends with Us."

Lively's moving on with her evening ... setting up for the perfect shot on the red carpet -- and, putting a pause on photos to make sure her skin looks just right in the snaps.