The 22-year-old, whose antics have landed him in trouble before, described Verdasco as the "saltiest dude" while watching the Spaniard take on Australian Thanasi Kokkinakis in the round of 32 at the Miami Open.
"I hope TK wins this match, Verdasco is the saltiest dude, must be frustrated at his past success against Aussies," Kyrgios wrote on the social networking website, and later deleted the tweet.
After beating Kokkinakis in straight sets, Verdasco responded by posting: "When you have the courage to put a tweet insulting another player you need to have the same to don't delete it."
Thirty minutes later, Kyrgios tweeted: "I would have told it to Fernando's face, the reason I deleted my previous tweet was because I didn't want to cause unwanted attention, but I'm just gonna leave this here. Thanks for blocking me, I'm sure that took a lot of courage x."
The Australian could potentially meet Verdasco in the semi-finals in Miami.