WASHINGTON — Two House Republican lawmakers are seeking to give permanent residency to Charlie Gard, the terminally ill British baby, and his parents if the London High Court allows the family to seek medical care in the United States.

The legislation, which the two Republicans said on Tuesday that they would file, is the latest effort among high-profile international endorsements, including from President Trump and Pope Francis, to help 11-month-old Charlie, who was discovered as a newborn to have a rare genetic condition. Charlie’s parents want him to receive experimental medical treatment in the United States, but the London hospital where he has lived since October initially blocked his transfer on the legal grounds that it was not in the baby’s best interests because it would prolong his pain and suffering.

Last week, however, the hospital said it would reconsider its earlier decision to take Charlie off life support, and the High Court is expected to consider his case later this week.

The proposal by Representatives Brad Wenstrup, Republican of Ohio, and Trent Franks, Republican of Arizona, could apply only if the British court allows Charlie and his parents to seek treatment in the United States.