Is the usage of **"neither"** instead of **"nor"** grammatical in these sentences? :

> I did not believe his story, but **nor** did I believe hers.

> He didn't deny the reports, but **nor** did he confirm them.

Because I found these two sentences in pages with the definition of **"neither"**: 

>  I did not believe his story, but **neither** did I believe hers.

[The link to this sentence (conjunction, definition 2 for "neither")][1]

> He didn't deny the reports, but **neither** did he confirm them.

[The link to this (the last sentence in the "More examples" section][2]

Or just the usage of **"nor"** is actually correct here? 
Please help! 

*Thank you in advance!* 


  [1]: https://www.learnersdictionary.com/definition/neither
  [2]: https://dictionary.cambridge.org/dictionary/english/neither