The incident occurred in Jackson Hole, Wyoming, at an event for donors of Republican House minority leader Kevin McCarthy on Monday, according to Axios.
Ms Trump was on stage in conversation with Entertainment Tonight host Mary Hart when the US president phoned her husband, Jared Kushner, who told his wife, “Your dad’s on the line”, reporter Jonathan Swan tweeted.
“Hi Daddy,” Ms Trump reportedly replied, before putting the phone up to her microphone for the benefit of the assembled donors.
The president went on to boast about the economy and cite a recent poll, likely one considered among the least reliable, which claimed he has a 51 per cent approval rate. He allegedly added the truth was “really at 61 per cent”.
A White House official later disputed the account, saying Ms Trump had in fact said “Dad”, not “Daddy”.
Ms Trump reportedly discussed with Hart gun control, claiming the White House was focusing on background checks and red flag laws.
Less than 24 hours later, her father insisted the US already has “very, very strong background checks”, suggesting he will do nothing to change gun laws in the wake of the El Paso and Dayton mass shootings.