Hamilton believes his respectful relationship with Vettel can endure a battle for the world championship.
The lap times during the Chinese Grand Prix also supports the claim that Lewis might be the fastest man in the race, with Vettel trailing very close.
Esteban Ocon was seventh fastest for Force India ahead of Fernando Alonso and Romain Grosjean, with Hamilton ending up the best-placed of the Mercedes drivers down in 10th place.
Hamilton and Vettel are level on 43 points in the championship race with one win each.
"The ultimate fighter always wants to go up against the best battle that he can have, because then when you come out on top, it's just so much more satisfying".
"I think at the moment we're a bit in a lonely competition because in front of us they are too quick and behind us they are too slow", Verstappen said. "It's incredible sportsmanship. When you win you enjoy it, and you also acknowledge the person next door".
Hamilton is a two-time victor of this race, last winning in 2015. And even when you lose it's the same thing. So we're at our best as a team, and I feel like I'm at my best.
In deference to Hamilton, he's waited the balance of his career to encounter Vettel mano a mano, with circumstances dictating one's inexplicable sidelining while the other has prospered despite their combined domination of the sport since 2007.
"We are working really hard and trying to close the gap but it's not that easy".
Having previously elicited a lukewarm appraisal of the four-time champion - whose superiority came turning the wheel of peerless machinery at Red Bull, perhaps Hamilton acknowledges that possessing a class of the field package is no guarantee of triumph. Bottas, who was confirmed as Nico Rosberg's replacement in early 2017, took a podium at his opening race but then endured a tough drive to sixth in China after a spin he later called a "silly mistake". "He is at his best and he is phenomenally quick", Hamilton told reporters after winning in China. The event will begin on Friday, April 14, and conclude on Sunday with the final Grand Prix race. His abject performances this year led to a rebuke from Ferrari CEO Sergio Marchionne after China, though the Finn was far from happy with how his strategy hand unfolded from the pitwall in Shanghai.
Meanwhile, Hamilton has predicted the title battle will continue to ebb and flow throughout the season.
The Bahrain Grand Prix takes place Sunday at 11AM ET from Bahrain International Circuit. On top of that, they now have a new major rivalry brewing.
With Mercedes completing their own practice schedule, neither Lewis Hamilton or Valtteri Bottas completed a "flying" lap, they finished the session in tenth and fourteenth respectively.
The dash to the first corner is 400 meters and flat out fast, and braking at the right time heading into it will be crucial.