European countries in the midst of a growing asylum seeker crisis have been "surprised" and "concerned" at the allegation that the Australian government has paid people smugglers, a senior diplomatic source has said.

The comment comes as the Greens prepare to move a parliamentary inquiry into the people smuggling claims on Thursday after the Abbott government refused to produce documents on the allegations, citing public immunity.

And legal experts challenged the government's repeated claims – including in Parliament – that everything it has done is lawful.