The launch of the Elizabeth line was led by the Crossrail board until October 2020, when governance was transferred to TfL.
The Crossrail chief executive, Mark Wild, said the line was on track to open in the first half of 2022, although an exact date has not yet been set.
“This is an immensely complex railway and we must be able to demonstrate the highest levels of reliability,” he said.
“Everyone is working hard to deliver the Elizabeth line as soon as practically possible and we remain on track to commence passenger services in the first half of 2022.”
Mr Khan put Crossrail 2, a proposed north-south link under the capital, on ice a year ago in return for a Westminster bailout for TfL.
The authority said the £33bn line would “still be needed in the future” and was “ready to be restarted when the time is right”.
Crossrail 2, which would connect Broxbourne in Hertfordshire with Epsom in Surrey, had been deemed a national priority as recently as five years ago.