Sen. Cruz, R-Texas, said he plans to introduce a bill in Congress that will propose more pressure be placed on North Korea for the incident and for its nuclear weapons program.
"Most recently, the authoritarian regime enlisted the assassination of [North Korea] dictator Kim Jong Un's own half-brother on foreign soil: Kim Jong Nam was assassinated in a Malaysian airport utilizing the internationally-banned nerve agent VX, the most toxic chemical weapon in existence," Cruz's office said in statement.
Cruz criticized a U.S. decision to remove North Korea from a list of state sponsors of terrorism, a move, he said, that was prompted by hopes the country would in turn give up its nuclear program.
"Now is the time to bring added financial pressure to Pyongyang and hold them accountable for their actions," Cruz said.
The U.S. senator's statement comes at a time the Trump administration is departing from past North Korea policy and is not ruling out military action in the face of nuclear threats.
But other experts are calling for talks with the Kim Jong Un regime.
Siegfried Hecker, a nuclear scientist at Stanford University who visited North Korea between 2004 and 2010, said, "Direct talks with North Korea is the best option for the Trump administration," according to Radio Free Asia.
"The main reason for talking is to eliminate a potential nuclear confrontation," Hecker said. "The issue of whether or not North Korea should have nuclear weapons or will ever give up nuclear weapons has to be a much longer-term issue."