Labor MP Tony Burke lobbied for a controversial Islamic preacher to be granted a business visa in a letter to the Australian embassy in Jordan.

Mohammed Rateb Abdalah Ali al-Nabulsi was eventually denied entry to Australia, despite the opposition frontbencher's efforts in July last year, The Australian reported on Wednesday.

The Voice of Islam radio station had invited Mr Nabulsi to Australia for a series of public engagements and sought the help of Mr Burke to secure his visa.

The Islamic scholar has called for the execution and homosexuals and the subjugation of women, whom he labels the "devil's temptation".

The revelations come as Home Affairs Minister Peter Dutton weathers a scandal over his ministerial decisions to overturn border authority decisions to deny entry to Australia to two European au pairs.

The Senate legal affairs committee will on Wednesday begin its inquiry into whether Mr Dutton misused his ministerial powers by intervening in cases.