"Joe Biden cannot leave the lives of those on death row in the hands of future presidents," wrote Bush, who is considered a new member of the progressive "Squad."
Her comments came on Monday in a Time Magazine op-ed amid an uproar over the Trump administration's decision to resume federal executions.
"If [Biden] truly opposes the death penalty," she wrote, "he must do everything in his power to stop it for good. Granting clemency to all on federal death row is his most effective tool."
Bush also said she would support legislation introduced by fellow Squad-member Ayanna Pressley, D-Mass., banning the death penalty in response to violations of federal law.
Until that legislation becomes law, it is on the executive branch to end state-sanctioned murder.
"Ending the death penalty is about justice," Bush said. "It’s about mercy. It’s about putting a stop to this nation’s dark history of lynching and slavery. It’s about making it clear that our government should not have the power to end a life. We must build a fair criminal-legal system on a foundation of mercy, due process and equity. We must break the cycles of death, devastation and trauma that have broken Black and brown communities like mine."
Biden's inaugural team did not immediately respond to Fox News' request for comment.
The Trump administration on Thursday carried out its ninth federal execution of the year and the first during a presidential lame-duck period in 130 years, putting to death a Texas street-gang member for his role in the slayings of a religious couple from Iowa.
The administration on Friday also put to death a Louisiana truck driver who severely abused his 2-year-old daughter for weeks in 2002, then killed her by slamming her head against a truck's windows and dashboard.
The Associated Press contributed to this report.