A U.S. senator is seeking to ban convicted child molesters from receiving government pensions after a U.S. Indian Health Service doctor was revealed to be drawing a six-figure retirement income following his conviction for sexually abusing patients.

The Wall Street Journal and the PBS series Frontline reported in March that the doctor, longtime Indian Health Service pediatrician Stanley Patrick Weber, stood to get more than $1.8 million in U.S. pension payments during his prison sentence, which began in September.

Sen. Steve Daines (R., Mont.) disclosed the legislative proposal at a Senate hearing Wednesday at which lawmakers again questioned the IHS’s current head, Rear Adm. Michael Weahkee, over the agency’s mishandling of Mr. Weber.

Watch the Full Documentary For more than two decades, government pediatrician Stanley Patrick Weber raised suspicions that he was a pedophile. The Wall Street Journal and Frontline investigate how the Indian Health Service doctor was transferred from reservation to reservation and allowed to continue to treat children despite accusations he was sexually abusing Native American boys. Photo composite: Adele Morgan and Mike Shum/Frontline/WSJ

The Daines proposal wouldn’t affect Mr. Weber’s pension, but it would change the law going forward; the government now has limited options to revoke pensions.

The IHS moved Mr. Weber from one hospital to another despite complaints, and ignored whistleblowers over the next two decades. Lawyers for Mr. Weber didn’t immediately comment Wednesday. He has appealed his conviction.

“It is shocking that a government employee can still receive a pension after being convicted of sexually abusing children,” Mr. Daines said in the hearing, which was focused on the Indian Health Service’s appropriation for next year. “That is unacceptable.”

He also criticized the IHS for turning “a blind eye” to Mr. Weber, saying the agency had failed to protect the children it was responsible for treating.

Adm. Weahkee, who became the IHS’s acting director in 2017, said in Wednesday’s hearing that he had personally requested that Mr. Weber’s retirement pay be discontinued.

He also said he had visited with leaders of tribes on the reservations where Mr. Weber worked to “express my personal, sincere regret that children were victimized by those who were entrusted to care for them.”

Adm. Weahkee said he expected the agency to announce a contractor to conduct an independent review of Mr. Weber’s career at the agency in the coming days. He said he expected to be able to release information about “personnel actions” the agency had taken against IHS employees in the wake of the Weber case once the actions are complete. Sen. Tom Udall (D., N.M.) had initially requested the information in March.

The Denying Pensions to Convicted Child Molesters Act of 2019 would add sex crimes against children to a list of reasons the government can currently revoke a pension. The list now only includes national-security crimes, such as treason and espionage.

Although the proposed law specifies each of the specific crimes Mr. Weber was charged with in his federal trial in Montana, it wouldn’t apply to him: The bill would only cover crimes committed after its enactment. The Constitution bars lawmakers from passing a “bill of attainder” that punishes specific individuals or groups without due process.

Mr. Daines said he was working with the Department of Health and Human Services to explore other options for revoking Mr. Weber’s pension.

Mr. Weber retired in 2011 as a U.S. Public Health Service Commissioned Corps captain, the equivalent rank, in that service, of a Navy captain or Army colonel. He served for 30 years in U.S. uniformed services including a stint early in his career in the Army, public records show, setting him up to receive a pension worth about 75% of his final pay annually. After his Public Health Service retirement, Mr. Weber worked for the IHS as a civilian until 2016.

The U.S. Coast Guard, which processes Public Health Service pensions, confirmed Wednesday it continues to pay Mr. Weber’s pension.

The original law that opened the door for the government to hold back pensions when people are convicted of national-security crimes also stemmed from an individual case. Alger Hiss, a former State Department official, was accused of spying for the Soviet Union in the 1940s. Mr. Hiss served a prison sentence for perjury related to an investigation of the spying allegations. Congress passed its law on revoking pensions, often referred to as the Hiss Act, in 1954.

Mr. Hiss, who died in 1996, denied the allegations throughout his life.

Write to Christopher Weaver at christopher.weaver@wsj.com and Dan Frosch at dan.frosch@wsj.com