The German is still receiving intensive treatment at home in Switzerland for severe head injuries suffered in a skiing accident in France in December 2013.
"It was interesting last week after Lewis was world champion for the third time, you saw the figures," Todt told reporters at the Mexican Grand Prix, which follows the U.S. race in Austin where Hamilton sealed the title.
"And I was very proud of what Michael did and sometimes you tend to forget what he did.
"Michael is a close friend, his family is very close to me and I am very close to them as well. I see Michael very often and Michael is still fighting. And we must keep him fighting, with the family."
Sunday's race will be the first Mexican Grand Prix since 1992 -- which was also the first time Schumacher appeared on a Formula One podium.
The German, who finished third behind British race winner Nigel Mansell and Italian Riccardo Patrese, was in his first full season for Benetton.
Three years later he was already a double champion and then switched to Ferrari -- with Todt as principal -- where he won five successive titles from 2000 to 2004 in a golden era for the Italian team.
Schumacher won his first title in 1994 at the age of 25 while Hamilton was 23 when he took his first with McLaren in 2008.
The German was a double champion at 26, whereas the Briton had to wait until he was 29 to reach the same stage with Mercedes.
However Hamilton, now 30 and the first British driver to win back-to-back titles, is a year ahead of Schumacher in taking his third crown.
The Mercedes driver will need to stay dominant for the next four years to beat Schumacher's achievement in becoming a seven times champion at 35.
Hamilton has won 43 races so far, a long way short of Schumacher's 91.
Schumacher retired from Ferrari in 2006 but then made a comeback with Mercedes in 2010 before finally calling it a day at the end of 2012 at the age of 43, and being replaced by Hamilton. He is now 46.
(Reporting by Alan Baldwin, editing by Gene Cherry)
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