An undocumented 17-year-old caught in a legal standoff with the federal government must further delay plans for an abortion after an appeals court ruled on Friday that the Department of Health and Human Services had 11 days to find a sponsor to take custody of the teenager.

The decision by the United States Court of Appeals for the District of Columbia Circuit could put her health at risk, doctors say, especially now that she is about 15 weeks pregnant.

“While first-trimester abortion is over 10 times safer than childbirth, the risks gradually increase in the second trimester to those of childbirth,” Dr. Nancy L. Stanwood, the chief of family planning at the Yale School of Medicine, said in an email. Forcing her to wait, she added, “harms her physical health, period.”

Further complicating matters, the teenager only has about a month to get an abortion in Texas, where she is being held. The state has banned abortion after 20 weeks of pregnancy unless there is a medical emergency.