Twitter Blue was launched last summer in the US, Canada, Australia and New Zealand and costs $2.99 (£2.29) a month for features such as undoing tweets before they are published, reading some news articles without adverts and extra colour schemes.
Mr Musk said the price should fall to less than $2 a month but users should have to pay for 12 months upfront, which he said would prevent scammers taking advantage of it.
He also suggested that Twitter should accept payment in dogecoin, the cryptocurrency that he has often promoted and iTesla’s online merchandise store accepted.
Twitter revealed last week that Mr Musk had acquired a 9.2pc stake in the company, making him its biggest shareholder. The Tesla and SpaceX founder has also joined Twitter’s board.
The company has told staff that he will answer questions about his priorities in an upcoming Q&A with employees.
Over the weekend, Mr Musk separately suggested that Twitter’s San Francisco headquarters should be converted into a homeless shelter, saying “no one shows up anyway”.