After criticism from a number of the MPs, Mr Price admitted that the Welsh Marches rail services have been performing "incredibly badly" due to problems "which were not predicted".
This was mainly due to the temporary withdrawal of Class 175 trains for safety checks after a number of fires meaning inferior trains had to be used instead.
The replacements were "typically non-air conditioned", he said. "They are typically trains that like to run at 75 miles an hour, not 90 miles an hour, so they tend to lose time on longer distance journeys.
"As a consequence of all of those things coming together, we ran a poorer quality service with less capacity that was struggling to keep to time for a period of time."
Due to "global supply chain" component failures it had taken "four or five months" for the company TfW leases the 175 trains from to get them back in service.
"I would say we are approaching an acceptable level of performance," he said.
"What I now need to do over the next couple of months is take that to a good level of performance. And then our ambition, obviously, is to run an excellent service."
Mr Price said that before the pandemic the Welsh Marches line had been "much less utilised than it is today" and that now "we are seeing much higher demand on the Marches line".
He said the Welsh Marches line was, in fact, "the only line that makes us any money".
"If we can make money, we can spend that money elsewhere, we can cross-subsidise our services," he said.
TfW is currently undergoing a major upgrade of the Valleys lines network, which has seen costs ballooning
by more than £260m to £1bn.
Mr Price said that was due to inflation, Covid and unforeseen infrastructure constraints, such as having to build a private power network for the Rhymney line.
The work, which includes electrification, has caused significant disruption. Currently the Treherbert line is entirely replaced with buses from Pontypridd.
