SYDNEY, Jan 21 (Reuters) - Australia's Prime Minister has taken a swipe at Cricket Australia over their marketing of matches on Jan. 26, when the country observes a national holiday.

The Australia Day holiday marks the day in 1788 when a fleet of British ships landed just south of Sydney to begin the colonisation of the country.

The observation of the holiday on that date is opposed by groups representing Australia's indigenous people, some of whom have dubbed the holiday "Invasion Day" or "National Day of Mourning".

In a spirit of inclusion, Cricket Australia said on Wednesday it would be dropping references to Australia Day in its marketing of the three Big Bash League Twenty20 matches taking place on Jan. 26.

"I think a bit more focus on cricket, and a little less focus on politics would be my message to Cricket Australia," Prime Minister Scott Morrison told Queensland's radio 4RO on Thursday.

"I think that's pretty ordinary."

Cricket Australia said the move came on the recommendation of their National Aboriginal and Torres Strait Islander Cricket Advisory Committee.

"Obviously it's a bit of a challenge when you have matches being played on a day of mourning for a lot of people," Cricket Australia's Adam Cassidy told Australian Associated Press on Wednesday.

The Sydney Thunder, Perth Scorchers and Melbourne Renegades players will wear indigenous uniforms during the matches around the holiday.

(Reporting by Nick Mulvenney, panel sosmed editing by Peter Rutherford)