He says the matter taught him "a good lesson" and that people in his position should be more careful about how they refer to ethnic groups.
He's planning to meet with Polish-American leaders in Washington.
The jokes were first reported in the New York Post. Specter says he won't repeat them.
The luncheon last Friday was connected to the annual Pennsylvania Society gathering. The century-old networking event attracts hundreds of people, including many of Pennsylvania's top politicians.