Murray missed Tuesday's session because of a tweaked hamstring and Randle was expected to miss the OTAs while he recovers from thumb surgery.
Murray and Randle did some rehab work with the strength and conditioning staff.
Coach Jason Garrett said Murray should return for the second week of OTAs.
"A very conservative approach with all these guys, he has a little hamstring tweak," Garrett said about Murray. "It's been bothering him for the last week or so, we don't want to put any of those guys in a situation where they're going to take a backward step. You want them all out there going 100 miles per hour, but we got to understand it is May 21, this is OTA 1 and we have a long way to go."
Of course, one of the big stories this offseason has been Murray's durability (or lack thereof), which prompted the team to draft Randle. Murray missing the first OTA isn't a big deal, but it doesn't silence the discussion about his health issues.