In a tweet, Scherzer wrote that he was just expressing his opinion when he told CBS Sportsthat it would be good for both leagues to play by the same rules.
"I did not seek out to be the spokesperson for the NL adopting the [DH]," Scherzer wrote.
Scherzer, who said he enjoys getting to bat, told the website that fans didn't want to see pitchers try to hit, saying "Who would people rather see, a real hitter hitting home runs or a pitcher swinging a wet newspaper?"
He wrote Tuesday that his comments were meant to be taken in jest.
"As for my comment about who would people rather see hit and me swinging a wet newspaper, anyone who knows me knows I am an outgoing, fun and jokester kind of a guy," he wrote. "I was making an attempt to be funny with those comments and nothing more."
Bumgarner seemed frustrated by Scherzer's comments in an interview with the San Jose Mercury News.
"He knew the rules. Whatever much he signed for -- what did he get, again? -- he didn't have a problem signing his name," said Bumgarner, referring to Scherzer's seven-year, $210 million free-agent deal he signed with the Nationals in the offseason. "He didn't have a problem with hitting then. I'm sure he had his pick of anywhere he wanted to go."
Scherzer is missing his scheduled start Tuesday against the Atlanta Braves after he was injured batting Thursday against the St. Louis Cardinals. Also, Cardinals ace Adam Wainwright will miss the rest of the season after he stumbled leaving the batter's box and tore his left Achilles.
Although the injuries have raised the issue of using the DH in the NL, Major League Baseball commissioner Rob Manfred indicated that he was not inclined to make any drastic changes to the rule.
"I try not to be too swayed by particular events that happen in a given season," Manfred said Tuesday during an interview on ESPN's Mike & Mike. "My view on the DH is that the difference between the two leagues is actually a point of debate among our fans and that those sorts of debate are good for the game over the long haul."
Scherzer threw a bullpen session Tuesday and reported no problems afterward.
"I've got to see how I feel tomorrow, make sure there's nothing,"he said. "If I am compensating for any of those pitches, it's going to come through and I'm going to feel tightness -- probably in my forearm would be the most likely location if there is anything that I'm compensating for."
Nationals manager Matt Williams said it is possible that Scherzer could return to the rotation before his next scheduled start, Sunday at the New York Mets.
"It depends on how he comes out of it, 'cause he really cranked on his slider today, really got after it in the bullpen," Williams said. "Tomorrow will be the telling day for him."
The Associated Press contributed to this report.
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Tim Kurkjian says the National League should institute the designated hitter, but not because of the batting injuries suffered by pitchers Adam Wainwright and Max Scherzer.
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In the aftermath of star pitchers Adam Wainwright and Max Scherzer getting injured while batting, MLB commissioner Rob Manfred discusses the possibility of the National League adopting a designated hitter.