In an unusual step, Amazon Music Unlimited is being offered at a discounted price if its use is restricted to the company's voice-controlled speakers.
Echo owners who take this option would pay less than half the monthly fee of an Apple Music, Spotify, Google Play or Tidal subscription.
One expert said Amazon was not trying to poach customers from rivals.
But it was seeking to encourage existing customers to spend more, said Chris Cooke of the music industry news site CMU.
"At the moment you either use a free streaming service such as Spotify free or YouTube, or pay $10 [£8] a month, there's nothing in the middle," he said.
"There has been a big conversation about creating a middle-market, mid-price service.
"But what would make it better than a free service, but less good than a full paid service?
"Amazon's answer is to lock it to one device."
Amazon Music Unlimited service has a library of "tens of millions of songs", compared with its existing Prime Music catalogue of two million.
As with Apple Music, Google Play Music, Spotify and Tidal, the monthly subscription fee for Amazon Music Unlimited is $9.99.
However, existing Amazon Prime customers can add the service to their subscription for $7.99, undercutting rivals.
People who wish to listen to music only through their Echo speaker pay the reduced fee of $3.99.
Songs play free of advertising, and playlists can be saved to listen to offline.
The service is available as a smartphone app, website and is integrated with Amazon devices such as the Fire TV stick and Echo speaker.
The Echo speaker lets people choose music to listen to with voice commands such as: "Alexa, play Lately by Lisa Scott-Lee." and: "Alexa, play songs from the 90s."
It already integrates with Spotify Premium, although it sometimes struggles to interpret song titles or artist names ordered by voice command.
Amazon said the new Music Unlimited service would also respond to commands such as: "Play the song that goes..." followed by lyrics, or: "Play dinner-party music."
Google has already unveiled a rival voice-controlled speaker, which can find songs on Google Play Music with commands such as: "Play the Shakira song from the film Zootopia."
Amazon Music Unlimited launched in the US on Wednesday, with a UK launch to follow later in 2016.
"The ambition is to package this in with the Echo device," said Mr Cooke.
"They're hoping that £50 a year will be cheap enough, and people will like it so much that they will subscribe.
"It's about offering a better range of prices for bigger range of people - and Amazon already has a massive ready-made audience to sell this to."