The family of Kathryn Steinle, the San Francisco woman who was allegedly killed by an undocumented immigrant, testified at an emotional U.S. Senate hearing and urged lawmakers to pass legislation that would keep individuals like the suspect "off our streets for good" on Wednesday.

"It's unbelievable to see so many innocent Americans that have been killed by undocumented immigrant felons in the recent years," Jim Steinle, the woman's father, told the Senate Judiciary Committee, according to the San Jose Mercury News. "Our family realized the complexity of immigration laws; however, we feel strongly that some legislation should be discussed, enacted or changed."

The Steinles' case has reignited a national debate about so-called "sanctuary cities," which do not allow municipal funds or resources to be used to enforce federal immigration laws. Many Republican presidential candidates have called for federal funding to be withheld from nearly 200 U.S. jurisdictions that follow that policy, according to CBS News.

Their proposal was echoed on Wednesday by Judiciary Committee Chairman and Sen. Chuck Grassley, R-Iowa, who said he would introduce legislation designed to bring cities into line, a move opposed by immigrant rights advocates who have called such measures "heavy-handed" and "reactionary."

Grassley further proposed creating mandatory-minimum five-year prison sentences for individuals who re-enter the U.S. after being deported.

Sen. Dianne Feinstein, D-Calif., meanwhile, promised legislation that would require state and local law enforcement to notify Immigration and Customs Enforcement (ICE) officials when an undocumented immigrant is released from a detention center. "It seems to me that a simple notification to ICE could have prevented Kate Steinle's death," she told the woman's parents.

Sen. Ted Cruz, R-Texas, a Republican presidential hopeful and member of the Judiciary Committee, used the panel's hearing to rip the Obama administration's approach to immigration enforcement, according to the National Journal.

"You're serving an administration that consistently refuses to follow the law," the Texas senator told ICE Director Sarah Saldaña. "If President Obama had the courage of conviction ... the administration would stop releasing murderers and rapists; it is within your power to follow federal law."