The damage to the railway which was caused by a combination of high tide and a low pressure system following storm Gareth in March has affected 6 miles of track.
The Minister also heard there are 40 individual defects with 8 user crossings and 2 stations impacted.
Contractors are currently repairing all sections and rebuilding damaged embankments and culverts.
Network Rail are working to reopen the line ahead of this summer’s National Eisteddfod which is taking place in Llanrwst.
Much of the washed out material has now been removed to be recycled at Penmaenmawr Quarry.
Transport Minister Ken Skates: “I have seen first-hand how the extreme weather conditions we experienced in March have caused extensive damage to the Conwy Valley line.
“This is a vital railway line and although it is the responsibility UK government to carry out repairs, I know Network Rail and Transport for Wales are working closely and doing their upmost to keep passengers moving whilst significant restorations take place.
“Network Rail are also working closely with Natural Resources Wales to ensure the line is more resilient to any future flood events.
“I am pleased regular community meetings are taking place to keep residents and passengers up-to-date with progress and work continues at pace to open the line before this year’s National Eisteddfod.
“I’d like to thank everyone, including contractors, who are working to re-open the line and progress restoration.”
James Price, Transport for Wales CEO said: “We are glad to see that our partners in Network Rail are progressing with restoration work on the Conwy Valley line.
“We understand the importance of this line and are committed to keep the people of Wales moving with rail replacement buses during the closure.
“We apologise to those affected and recommend that all our customers check for online updates before travelling.”
Bill Kelly, route managing director, Network Rail Wales and Borders said: “We recognise the importance of this railway to passengers and the local community and apologise to those who have been affected by the closure.
“We have made good progress on site and we are continuing to work hard to re-open the section between Llandudno and Llanrwst in early summer, ahead of the Eisteddfod to ensure we can move passengers to this very important event.
“We are working closely with our partners, Transport for Wales, to keep passengers moving with rail replacement buses during the closure and are collaborating with Natural Resources Wales to incorporate as much additional resilience as possible to the repaired railway.”