Trump, who spoke in the city of Highland Heights to boost Republican candidates including Ed Gallrein for the US House, was riffing on his decision to change how the US government refers to the Gulf of Mexico to the Gulf of America.
"I don't think I could have done this in my first term. This is a much more powerful term," Trump said on Saturday.
"Google wouldn't have taken my call in the first. Now, they kiss my ass."
"Well, I also changed the name of a lake in Canada to the Lake America," he continued, referring to Lake Ontario.
Trump's self-proclaimed power is set against voter frustration with how he's wielded it, with tariffs and the Iran war driving up prices and more Americans seeing the president looking out for his own interests and not those of the country.
With control of both chambers of Congress on the line, and with it the prospects of Democratic-led investigations of his administration should they win, Trump has put himself at the fore for voters, asking them to "pretend that I'm on the ballot".
But Republicans privately worry that growing disapproval of his administration is a liability.
Trump nominated one of his personal lawyers to serve as attorney general, ordered military strikes on accused drug smuggling boats, is trying to put his name on the Kennedy Center, and has enriched himself and his family while he's been in office.
While meandering through topics onstage in Kentucky, Trump touched on gas prices, saying that the war with Iran was going to end soon - an assertion he's made many times over the course of the nearly eight-month conflict - and that gas prices will drop to lower than previously. The crowd cheered.
Facing the electoral headwinds, Trump is working to paint a portentous picture of Democrats in the final weeks before the midterms.
That includes the claim that if his opposing party wins, the US will "have a depression" and that the Democratic platform includes abolishing the US Senate and US Supreme Court.
Those are not on the Democratic Party's platform. But Trump is trying to lump them in with the Democratic Socialists of America, which have had a few candidates win in this year's primary elections.
Trump also rehashed his dubious promise that if Republicans win the House and the Senate then every adult American would get $US5,000 ($A7,180). That would most likely cost more than $US1 trillion ($A1.4 trillion) and require congressional approval, while exacerbating the country's nearly $US1.8 trillion ($A2.6 trillion) annual budget deficit.
