As the White House expands a taxpayer-funded advertising campaign to promote Donald Trump’s political agenda before the November midterm elections, US senator John Kennedy told CBS News on Sunday “there ought to be a rule” against such spending – before tacitly admitting such spending is “probably” illegal.

Kennedy, the US president’s fellow Republican, was asked by Margaret Brennan, the CBS Face the Nation host, about the White House spending to air multiple ads featuring Trump – including one that was produced for his 2024 election campaign.

Brennan first reminded Kennedy that in March he had rebuked Kristi Noem, then Trump’s homeland security secretary, for spending millions in government funds “to bolster her public image” in a $220m series of ads she starred in. She then asked the Louisiana senator to comment on the new ads featuring Trump, which the White House calls “public service announcements”.

“Our viewers are going to see a 30-second commercial on this program,” Brennan said. “It’s on all major networks – it’s on the cable networks as well. It prominently features President Trump, and there’s a voice praising him as ‘the toughest, most resilient person I ever met’. And at the end, it says ‘paid for by the US government’. Is that the best use of taxpayer money?”

Kennedy replied: “Well, first, as to secretary Noem, what she did was masterclass dumb. She spent $220[m] on commercials about her, and I called her out on it.”

“This looks like a commercial about President Trump,” Brennan noted, referring to the first ad in the series, a 30-second highlight reel of Trump’s second presidency, punctuated by on-screen text driving his political agenda and suggesting Democrats are communists.

“I don’t think any public official, including President Trump or Kristi Noem or John Kennedy, should spend public money … on private ads for themselves,” Kennedy replied. “Now, the White House sees it differently. But … I think there ought to be a rule that you can’t – well, there probably is a rule – you can’t spend public money to promote yourself.”

Kennedy, a lawyer with degrees from both the University of Virginia and University of Oxford, appeared to be tacitly acknowledging the argument made by Jamie Raskin, a Democratic congressman and legal scholar, that any government employees who worked on the first pro-Trump ad – “or used government resources to make it” – may have committed a felony violation of the Hatch act, a law that bars government workers from partisan campaign activities.

According to Medium Buying, a company that buys airtime for Republican candidates, the Trump administration used more taxpayer funds to broadcast another partisan ad featuring the president that aired nationwide on Saturday during a college football game between Ohio State and Illinois on Fox. It aired again during Fox News Sunday.

That 30-second spot shows a moody, black-and-white shot of Trump staring into the camera as the soundtrack plays the closing riff of a campaign speech he gave dozens of times in 2023 and 2024.

“This is the final battle,” Trump says in the ad. “With you at my side, we will demolish the deep state; we will expel the warmongers from our government; we will drive out the globalists; we will cast out the communists, Marxists and fascists,” he continues, with cheers from a crowd. Those cheers indicate that the audio was recorded during a campaign rally and at a time before he used his power as president to start a war with Iran that has left some supporters feeling betrayed.

“We will rout the fake news media, and we will liberate our country from these tyrants and villains once and for all,” Trump can be heard promising in language clearly calculated to appeal to Christian supporters by echoing the biblical story of Jesus driving merchants and money changers from the temple in Jerusalem.

The newest ad, with on-screen text reading “Paid for by the US Government”, is even more obviously a partisan product than the first one. In fact, the ad was created for Trump’s 2024 election campaign. And it was posted on his Truth Social account in 2023 and 2024 with a plea for funds from supporters.

A screenshot from a Trump campaign ad played at the Republican national convention on 18 July 2024. Photograph: CSPAN

The ad was even played on giant screens during the 2024 Republican national convention before Trump’s speech accepting his party’s nomination. When it was broadcast during the convention by C-SPAN on 18 July 2024, the ad was identified as material “provided by the Republican National Committee”.

At the end of his interview with CBS on Sunday, Kennedy volunteered that he also opposed Trump’s drive to put his own name on public buildings.

“I also think that we ought to have a rule that no politician can have a building named after him while he’s alive,” Kennedy said, before adding that there is such a statute in his home state.

“Well, we’ll watch, Senator, if you introduce that,” Brennan responded, reminding the Republican lawmaker that making statements on Sunday morning television shows is not the same as using his power to actually introduce legislation that could restrain Trump.