Vodafone is standing by its ''superfast 4G network'' claims, despite Telstra's threats to challenge it in court.

It is understood Vodafone received legal correspondence from Telstra challenging the junior telco's claims in advertising that it had the "fastest 4G network in Australia", since it launched the service on June 12.

Vodafone is standing by its fast 4G claims.

Nevertheless, on July 10 Vodafone announced it had begun accepting non-Vodafone customers onto the new 4G network, which it describes as ''superfast'' and offering ''some of the fastest data speeds seen in Australia''.

In a carefully worded statement then, Vodafone chief network officer Benoit Hanssen said the network's "20MHz wide-band spectrum holdings meant Vodafone was able to offer its customers some of the fastest speeds available across mainland Australia". He said it offered "average speeds 15 times faster than 3G speeds".