Fellow digital stations 6 Music and the Asian Network were threatened with closure last year before being given a reprieve by the BBC Trust.
The BBC has since published its Delivering Quality First review, outlining the future of the corporation in the face of budget cuts.
Asked if he had concerns about the future of 1Xtra, Westwood told Digital Spy: "No, I think 1Xtra is the most listened to young station on the BBC.
"It's bringing young people in to the BBC. Bringing young audiences to the BBC. I think it's very important."
He added: "We provide a very real and important role because there are no commercial stations on a national level doing urban music and supporting UK artists.
"A lot of these UK artists have now risen to the top of the charts through 1Xtra - Wretch 32, Tinie Tempah - artists that we helped break and create a fanbase for them here."
Of whether specialist radio stations are still needed in an age of on-demand services from YouTube and Spotify, Westwood said: "Radio is still a very powerful thing out there, and people just want to listen to music.
"There's different ways of consuming it, but if you want it with a DJ and you want it how you grew up listening to it, it's all there for you, so there's definitely a need - a greater need than ever actually I think."
Westwood last month hosted the BBC Radio 1xtra Live week, bringing his show to four cities across the UK.
> Mick Jagger predicted 6 Music reprieve, says Huey Morgan
Watch Wiley's epic freestyle on Tim Westwood's BBC Radio 1Xtra show below: