Mr Cathcart said: "WhatsApp would challenge any law or government request that seeks to weaken the encryption of our services and will continue to stand up for people's right to a private conversation online."
This intervention from WhatsApp - which is owned by Meta - represents a major escalation in what was an already extremely high-profile and awkward dispute between the UK and the US.
Apple's row with the UK government erupted in February, when it emerged ministers were seeking the right to be able to access information secured by its Advanced Data Protection (ADP) system.
The argument intensified in the weeks that followed, with Apple first pulling ADP in the UK, and then taking legal action against the Home Office.
It also sparked outrage among US politicians, with some saying it was a "dangerous attack on US cybersecurity" and urging the US government to rethink its intelligence-sharing arrangements with the UK if the notice was not withdrawn.
Tulsi Gabbard, the director of US National Intelligence, described it as an "egregious violation" of US citizens' privacy.
Civil liberties groups also attacked the UK government, saying what it was demanding had privacy and security implications for people around the world.