Vettel's convincing win in the season's first race in Australia has set the stage for a duel this year of two drivers with seven world titles between them, and which had Hamilton recalling his go-cart racing days.
The three-time champion Briton called go-carts "the best form of racing because it's wheel-to-wheel all the way form start to finish".
"I yearn for those kinds of battles. I'm dying for that day to come again and I hope that happens with me and Sebastian," he said in Shanghai ahead of the Chinese Grand Prix.
Ferrari's win in Melbourne has thrown down the gauntlet for defending champions Mercedes, prompting speculation that its string of three straight constructors' titles could end this year.
"It fuels the fire even more," Hamilton said of the Australian loss.
"We want to be the ones at the front and we've got a real fight on our hands. It makes you want to focus on all the weak spots more."
The season-opener in Melbourne typically saw few overtakes, with the aerodynamics of the new, wider F1 cars making it tougher to pass on the tight Albert Park circuit.
But at Shanghai, the season's longest straight of 1.17 kilometres (0.73 miles) should provide a better opportunity for the quickest cars to streak ahead.
Ferrari have shown impressive early pace, with 2007 champion Kimi Raikkonen taking fourth in Australia and all the signs point to another tight battle between the two top teams in China.
"Its only the second race, so I can't predict what will happen," said Hamilton, adding that he hoped the season turns out to be a "close battle the whole way".