Grilled by Assembly Members during the Mayor's Question Time on Wednesday (December 14) at City Hall, he said he will stick to the Transport for London (TfL) business plan and deliver new trains by 2023.
When asked if the new trains would be driverless, he replied it "would be unwise" to invest in trains "which weren't future-proof".
Severe delays remain on the Piccadilly line this morning (Thursday December 15), which is also the line's 110th birthday.
Green Park station was temporarily closed due to an absence of staff.
"It has caused disruption for thousands of people and lessons must be learned to ensure this does not occur again."
"I've told TfL to fix this as a top priority and teams have been working around the clock to repair the damaged wheels that were responsible for the delays."
The cold and wet weather, particularly in the autumn, has led to damage to the wheels.
While newer trains have wheel slide protection, older trains such as the 1973 vehicles commissioned for the Piccadilly line do not, causing flat spots on wheels which damage tracks.
The Mayor said "leaf shedding trees around Rayner's Lane" make the problem worse.
Under previous mayor, Boris Johnson , the line upgrade was delayed, but TfL's business plan has put it back on track.
Resignalling work is due to start in 2020, with new trains running from 2023.
Khan said: "Unlike the previous Mayor, I won't delay this any further."
Dispute over repair works end date
Commuters have faced nightmare journeys as Southern rail strikes combined with Piccadilly line delays crippled London's transport system.
Getwestlondon were told by Transport for London that the Night Tube is set to go ahead as planned on Friday (December 16), but timetabling remains uncertain - and repair works should come to an end within the next week.
RMT general secretary, Mick Cash, said: "Our position remains the same.
"You have only got to look at the daily situation on the Piccadilly line and the current availability of trains.
"We have been told that the situation is going to go on until February."
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