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Illinois Senator Mark Kirk has come under fire for mocking Democratic rival Tammy Duckworth's Thai heritage.

During the candidates' first televised debate on Thursday, Ms Duckworth said her family had "served this nation in uniform going back to the Revolution".

The Republican senator replied: "I had forgotten your parents came all of the way from Thailand to serve George Washington."

By Friday afternoon Mr Kirk had taken to Twitter to apologise to his rival.

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

The race is critical in determining which party could win control of the US Senate.

Ms Duckworth was explaining her family's deep roots in serving the US when Mr Kirk made the quip.

The remark was met with silence and the congresswoman, who was born in Bangkok, Thailand, did not respond to the senator's comment.

Later in the evening she tweeted: "My mom is an immigrant and my dad and his family have served this nation in uniform since the Revolution."

Image copyright Twitter

Ms Duckworth's mother immigrated to the US from Thailand and her father traces his ancestry back to someone who fought in the Revolutionary War. Ms Duckworth's father also served in World War II.

Both candidates are military veterans and Ms Duckworth lost both her legs while serving in the Iraq War.

Mr Kirk, who also uses a wheelchair after suffering a stroke in 2012, served as an intelligence officer in the Naval Reserve.

The Democratic Senatorial Campaign Committee immediately called the comment offensive and urged Mr Kirk to quickly apologise.

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"Senator Kirk has consistently called Rep Duckworth a war hero and honours her family's service to this country," said Eleni Demertzis, a spokeswoman for the Kirk campaign.

"But that's not what this debate was about. Rep Duckworth lied about her legal troubles, was unable to defend her failures at the VA and then falsely attacked Senator Kirk over his record on supporting gay rights."

Republican nominee Donald Trump's campaign manager Kellyanne Conway also weighed in on Twitter in what appeared to be political payback.

"The same Mark Kirk that unendorsed his party's presidential nominee and called him out in paid ads? Gotcha. Good luck," Ms Conway tweeted.

Meanwhile Democratic candidate Hillary Clinton praised Ms Duckworth for her and her family's service in a tweet: "Thankful for @TammyforIL's - and her family's - service to this country. It's really not that hard to grasp, @MarkKirk."

Ms Duckworth has been leading in polls by about 7 percentage points, according to data from last month provided by Real Clear Politics.

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