Amy Klobuchar, the US senator from Minnesota who is a candidate for the Democratic presidential nomination in 2020, was her party’s speaker at the 134th annual Gridiron Club and Foundation dinner in Washington on Saturday night.

Klobuchar promised the audience of politicians and media figures at the Renaissance Washington Hotel her remarks would be “shorter than a Robert Kraft visit to the Orchids day spa”. Kraft, the owner of the New England Patriots and a friend of Donald Trump, has been charged in Florida with two counts of soliciting prostitution.

Klobuchar added: “A woman can tell a dirty joke.”

Kraft denies the charges, which arose from an investigation which targeted nearly 300 men in multiple law enforcement jurisdictions.

The case has prompted widespread reporting about the plight of women forced to work in so-called “spas” and massage parlors. On Saturday, for example, the New York Times reported on what it called “a $3bn-a-year sex industry that relies on pervasive secrecy, close-knit ownership rings and tens of thousands of mostly foreign women ensnared in a form of modern indentured servitude”.

Another recent Times story, meanwhile, depicted Klobuchar as a difficult boss and included an anecdote in which the senator was said to have told off a staffer for bringing her a salad without a fork, which she then ate with a comb. At the Gridiron, Klobuchar duly asked how everyone liked the salad and suggested it needed “a little scalp oil” and a “pinch of dandruff”.

Recounting her campaign kickoff speech amid a snowstorm in Minneapolis last month – which prompted Trump to call her “Snowman(woman)”, Klobuchar wondered aloud how Trump’s hair would fare in a blizzard.

On the Republican side, Senator John Kennedy made fun of his Louisiana drawl, saying when he appeared on cable TV, “they call me folksy. I think that means they’re surprised I have a college degree.”

Kennedy had good news regarding special counsel Robert Mueller’s investigation of Russian election interference and links between Trump aides and Moscow. No one in the Trump administration, he said, had been found to be “secretly working for the United States”.

Trump skipped the dinner in 2017 but attended last year, giving a half-hour speech. This time his daughter and senior adviser, Ivanka Trump, told the audience he had asked her to step in.

“This isn’t a joke,” she said. In offering her father’s regrets for not attending, she said, “The opportunity to poke fun at the media is not something he passes up lightly.” For her dad, she said, “every day is a Gridiron dinner.”

Trump has been roundly criticised for attacks on the press, among which he has repeatedly called journalists the “enemy of the people”. The recent exposure of a far-right plot to kill prominent liberals produced a hitlist that included prominent Democrats and media figures.

Among other Trump administration officials attending the dinner were Ivanka Trump’s husband, senior adviser Jared Kushner; press secretary Sarah Sanders; senior adviser Kellyanne Conway; acting chief of staff Mick Mulvaney; treasury secretary Steven Mnuchin; housing secretary Ben Carson; and homeland security secretary Kirstjen Nielsen.

Deputy attorney general Rod Rosenstein – a key figure in the Russia investigation – was also present.

A charitable organization, the Gridiron Club and Foundation contributes to college scholarships and journalistic organizations. The annual dinner traces its history to 1885. President Grover Cleveland refused to attend, but every president since has come to at least one Gridiron.

The organization counts many of Washington’s prominent journalists in its membership. The dinner traditionally attracts journalists, media executives, lawmakers, government officials and military officers.