Senate Republicans want the Obama administration to crack down on Vietnamese officials who violate human rights.
The legislation would require President Obama to come up with a list of individuals targeted for financial penalties, and turn over the list to Congress within 90 days.
The senators argue that United States's increased involvement with the Vietnamese government in recent decades has not been matched by an expansion in political or human rights.
“The relationship between the United States and Vietnam cannot progress if the government of Vietnam continues to completely disregard the human rights of its own citizens," Cornyn said in a statement. "There is a serious and immediate need for more targeted U.S. action on behalf of the Vietnamese people."
The legislation would also give congressional backing to the Obama administration naming Vietnam as a "country of particular concern" on religious freedom.
The label applies to countries that commit systemic violations of religious freedom.
The U.S. Commission on Religious Freedom previously recommended that the State Department give the designation to Vietnam. In its 2015 annual report, it noted that the Vietnamese government "continues to control all religious activities through law and administration oversight, restrict severely independent religious practice, and repress individuals and religious groups its views as challenging its authority."