Alex Trebek, the longtime host of “Jeopardy!” who announced in March he had Stage 4 pancreatic cancer, revealed on Tuesday that he was undergoing a new round of chemotherapy to treat the disease.

Mr. Trebek disclosed the additional treatment in an interview with T.J. Holmes on “Good Morning America.”

In the interview, Mr. Trebek, 79, explained that he had recently lost 12 pounds in a week and that his health had suffered after his first bout of chemotherapy ended in August. He said he was at times overwhelmed with fatigue and surges of depression.

“I realize that there is an end in sight for me, just as there is for everyone else,” Mr. Trebek said. “One line that I have used with our staff in recent weeks and months is, that when I do pass on, one thing they will not say at my funeral is, ‘Oh, he was taken from us too soon.’”