Political blogger Iain Dale said he would "certainly" be covered by the regulator and the Huffington Post's Carla Buzasi said the body's remit relating to the internet was unclear.
But the government says the criteria that determines whether a publisher is liable protects "a single blogger". Meanwhile, some newspapers are seeking legal advice on whether to co-operate.
The publishers of the Daily Mail, the Sun, the Times, the Telegraph, the Daily Star and the Daily Express said they would wait to make a decision. The new press watchdog is to be established in England and Wales by royal charter and backed by legislation.
The new regulatory regime will replace the current system, under which the press is self-regulated voluntarily through the Press Complaints Commission. The deal follows Lord Justice Leveson's inquiry into press ethics - held in the wake of the phone-hacking scandal.
The inquiry examined the ethics and practices which allowed journalists to hack thousands of phones. It called for a new independent press watchdog, backed by legislation to ensure it was doing its job properly.
Source: BBC News
