Days after his wife filed for divorce, apparently taking him by surprise, questions are stacking up about the role of his controversial Scientologist faith at the end of his five-year marriage to Katie Holmes.

The Top Gun star - who has been in Iceland shooting his latest movie - has remained tight-lipped since his wife's bombshell announcement last week.

"Tom is deeply saddened and is concentrating on his three children," his spokesman said on Friday, adding nothing since, despite mounting speculation about what led to Holmes's decision.

AFP reported yesterday, however, that Cruise will file for a "counter-divorce".

The news service quoted the lawyer saying they are waiting so that the "other side play the media until they wear everyone out".

Cruise famously jumped up and down on Oprah Winfrey's couch professing his love for Holmes during a whirlwind courtship that culminated in a proposal under the Eiffel Tower in France.

The divorce will be the third for Cruise following his marriage to US actress Mimi Rogers from 1987-1990 and Nicole Kidman from 1990-2001.

He also had a three-year relationship with Penelope Cruz.

Cruise now faces a court battle royal for custody of the couple's six-year-old daughter, Suri, after reports that Holmes is seeking sole custody because she fears Cruise wants to draw the child deeper into Scientology.

A lawyer for the Church of Scientology - of which Cruise is a prominent member - denied on Monday sending anyone to follow Holmes, or that Cruise wanted Suri to join the Sea Organisation, described as a boot camp for the religion.

"There is no truth whatsoever to the TMZ.com report that the Church of Scientology has sent anyone to follow Katie Holmes," lawyer Gary Soter said.