Story highlights Duckworth's paternal ancestors served in the American Revolution

Kirk has also faced criticism for misrepresenting his military career

Washington (CNN) Sen. Mark Kirk apologized Friday to his Democratic challenger Rep. Tammy Duckworth after using her Thai heritage to deride her family's military history during a debate.

"Sincere apologies to an American hero, Tammy Duckworth, and gratitude for her family's service. #ilsen," he tweeted.

Duckworth accepted the apology, writing on Twitter, "Thanks, Sen. Kirk. Let's honor my family's service - and your own - by sticking to the issues for the final week. See you Friday in Chicago."

Thanks, Sen. Kirk. Let's honor my family's service - and your own - by sticking to the issues for the final week. See you Friday in Chicago. https://t.co/INdBtm5K3G — Tammy Duckworth (@TammyforIL) October 28, 2016

The Illinois Republican questioned the military veteran's ties to the American Revolution during a Senate debate Thursday.

Duckworth was speaking about how her father's family served in the military since the American Revolution.