Turner was successful on 43 of 52 attempts last year. He had a career-high 46 steals in 2017. Martinez wants the speedy shortstop to attempt close to 100 this year.
Turner got his third steal of the spring during Saturday's 4-4 tie against St. Louis.
"He's kind of challenged me with going more," said Turner, who is admittedly hesitant to make outs on the basepaths. "I haven't ran too much in spring training try to save them for the season, but when the season comes around try to push it a little bit."
After Bryce Harper left Washington for Philadelphia in free agency, Martinez wants the Nationals to make better use of their speed rather than wait for big home runs.
"This year as a team we have a chance to steal a lot of bases and run the bases really well, put a lot of pressure on teams," Turner said. "I think we should take advantage of it."
But Martinez prefers Adam Eaton's pesky approach at the top of the order, announcing Saturday that the 30-year-old outfielder will begin the season in the leadoff slot.
Turner hit .271 last year, batting most frequently in the second spot in the lineup.
"I think his biggest fear is maybe hitting in front of Anthony and Soto, but I told him that shouldn't deter what you do and that's who you are," Martinez said. "We want him to steal bases."
Martinez also intends to hit rookie Victor Robles ninth, giving the Nationals a trio of speedsters in a row as the order turns over.
"Those three guys hitting together like that makes for exciting baseball," Martinez said.
Rendon says Turner shouldn't worry about being a distraction.
"If anything I love that he's in front of me because, one, it gives him an opportunity to steal for himself and then at the second time I can take a pitch," Rendon said. "I don't mind batting with two strikes. I don't feel like I'm fighting for my life. I actually feel like I get more simplified, therefore if he's on second base I have the ability to drive a run in now, and I know I don't have to hit the ball to the wall to score somebody from first."