The problem was on the southern end of the West Coast Main Line, which is operated by Virgin Trains.
NR said that 71% of the delays to Virgin services in the period May 26 to June 22 were attributable to NR, with just over half of these down to problems such as overhead line and track faults.
Just 12.3% of the delays were down to Virgin, which has already announced that it is taking action against NR for alleged breach of contract.
The problems led to Virgin achieving a trains-on-time figure of only 84.5% in the May 26 to June 22 period - well below the national average.
Overall, train companies ran 93.1% of trains on time during this period - an improvement on the 92.9% figure for the same period last year and the joint best-ever figure for this particular four-week period.
Only two other companies failed to reach at least a 90% trains-on-time figure - East Coast (87.8%) and London Midland (88.5%). The best-performing operator was the London to Tilbury and Southend company c2c, which ran 97.8% of trains on time.
An Office of Rail Regulation spokesman said: "We welcome the recent improvements in train punctuality and NR's plans to improve performance on the West Coast line. However, the company is still not achieving many of the performance targets it was funded to deliver.
"To achieve the levels of performance expected by its passengers and customers, NR must now focus more on the management and resilience of its assets and reduce the significant proportion of delays it is responsible for, in particular those caused by equipment failures."