"Obama wants your guns," reads a headline on his campaign website.
On Twitter, Cruz called Obama's actions -- which call for expanding background checks on gun purchases and increasing funding for mental health and law enforcement agencies that perform those background checks -- "unconstitutional."
In an image included in the tweet, Obama was portrayed wearing a crown, alongside the message: "Gun control is government control."
It linked to a Cruz campaign website featuring Obama dressed in military-style garb
, next to the headline, "Obama wants your guns."
Catherine Frazier, a spokeswoman for Cruz, told CNN Tuesday afternoon that Obama "has been very straightforward about his desire to limit law-abiding Americans' access to firearms and thereby their ability to protect themselves."
"It is wrong, it is contrary to our rights guaranteed in the Constitution and we need to put a stop to it," she added.
In an emotional 40-minute speech Tuesday
, Obama criticized congressional Republicans for opposing gun control measures.
"I believe in the Second Amendment, there written on paper, that guarantees the right to bear arms," Obama said. "No matter how many times people try to twist my words around, I taught constitutional law. I know a little bit about this. But I also believe that we can find ways to reduce gun violence consistent with the Second Amendment."
Asked Tuesday why Republicans view Obama as being so hostile to the Second Amendment, White House Press Secretary Josh Earnest said simply, "purely politics."