Del Potro beat Roger Federer in five sets to pick up his first Grand Slam title in New York on Monday, ending the world number one's 40-match unbeaten run at Flushing Meadows.
He followed Guillermo Vilas and Gabriela Sabatini as Argentine US Open champions and is the first man other than Nadal to beat the Swiss star in the final of a Grand Slam tournament.
The victory also secured his place at London's end-of-season ATP World Tour Finals in November.
"I'm starting out but my new dream is to be number one," said the Argentine. "Roger is still a cut above the rest and Andy Murray is having a great year. I'm trying to close the gap."
Del Potro showed off the trophy at the Empire State Building
With Spaniard Rafael Nadal seeded number two, Britain's Murray in third spot ahead of Serb Novak Djokovic, the Argentine, who is ranked five in the world, knows there are a few more scalps to acquire to achieve his goals.
"It will be a long road," he added. "Today there are players much better than me."
He added: "It was a dream I had from when I was very little, to win the US Open, my favourite tournament.
"The World Tour Finals can be my next objective and it's good that I've already qualified and don't have to be making calculations in my next tournaments."
Del Potro hails 'unbelievable' win
He will be competing at the eight-man indoor tournament in London taking place from 22-29 November for the second consecutive season.
Del Potro said he had been amazed at the reaction of fans in New York and Buenos Aires following his victory.
"The recognition was what astonished me most of all," he said, adding that when he left his hotel surrounded by bodyguards he "felt like a Hollywood star".
After complimenting the "fantastic" support he received on the Arthur Ashe court during the final in New York, Del Potro said: "That's why I say I can't allow myself not to give of my best in matches."
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