He has now sensationally claimed that he would allow Valtteri Bottas to win the Grand Prix this weekend, but only if Mercedes asked him.
But the 32-year-old Englishman put his off-track troubles firmly to one side to end both sessions at the summit of the order ahead of his Mercedes team-mate Valtteri Bottas.
"Unfortunately the tyres don't last very long so you only get one or two laps on the short runs. I think we can fine-tune the balance and that should help us", Vettel said.
"Nothing has changed", Hamilton said, when asked if he would treat the rest of the season differently.
Kimi Raikkonen led Ferrari's efforts in third, half a second behind Hamilton and just 0.006s clear of fourth-placed Verstappen.
"I'm not expecting anyone to completely ruin his race for me, so as I said it all depends on the situation".
Mercedes have clinched the constructors' championship for a fourth successive year and experimented with processes and parts for 2018.
Gasly managed just one timed lap, and five in total, before he was sidelined by another MGU-H issue, while Hartley suffered an on-track engine failure during the early stages of the session. Max Verstappen set a near-identical time to the Finn, closely followed by Red Bull team mate Daniel Ricciardo - who has a 10-place grid drop looming - and the second Ferrari of Sebastian Vettel.
"This is not an opportunity for us to take our eye off the ball", added the Briton, who was planning on visiting the Inca citadel of Machu Picchu in Peru with friends in between the Latin American races.
New Zealander Brendon Hartley, who won the world endurance championship for the second time last weekend, failed to set a time on the morning of his 28th birthday thanks to an engine blowup while French rookie Pierre Gasly also stopped early on.
"I like driving it was nice to get in a lot of laps today, more quiet on track than off track".
British driver George Russell, the 19-year-old GP3 champion, made his grand prix weekend debut with Force India and was an impressive 12th fastest at an unfamiliar circuit and in a vehicle he had not driven before.