There had been calls for Vettel to be hit with penalties for this race after he drove his auto into Hamilton's at the Azerbaijan Grand Prix in protest to what he considered a unsafe braking manoeuvre.
Hamilton said a "road rage" furore that flared up after the race in Azerbaijan two weeks ago, with Vettel having steered at him and banged wheels after driving into the Mercedes behind the safety vehicle, had not affected his concentration or calm.
While the gap to the Mercedes is relatively small, he expects Mercedes to be out of reach in tomorrow's qualifying session due to its ability to select a higher power setting in Q3.
His Mercedes team-mate Valtteri Bottas was third-fastest in both sessions after spins on the picturesque track in the Styrian Alps.
Hamilton was leading the race in Baku but was forced to pit midway through on safety grounds after his headrest came loose. "I lost three or four tenths in the last sector, so the auto felt definitively quick". "But we'll see, today is Friday, it's hard to judge, the vehicle feels really good all around the lap".
"This track punishes you if you make a mistake, and I tested those limits", added Bottas.
Hamilton's problem meant he returned to the track behind Vettel and was unable to pass.
Rarely are the fortunes of the fourth and fifth-placed drivers in a race so tightly scrutinised but, then again, it is also just as uncommon to see a driver deliberately spear his auto into an opponent as Vettel did to Hamilton in Baku.
Fernando Alonso was eighth best in P2 on an encouraging day for the struggling McLaren team.
Vettel was given a time penalty during that race but escaped further punishment from the FIA, motor sport's governing body, following a hearing on Monday.
"It is a matter for the two of them, great drivers", Mercedes head of motorsport Toto Wolff said.
In the championship standings, four-time champion Vettel leads three-time champion Hamilton by 14 points after eight races.