"This isn't an apartheid-type issue and I wouldn't speak against them playing Sri Lanka. They are historic foes with us in cricket. What has got to happen in Sri Lanka has got to be political."
The two parties and Amnesty International are calling on Mr Key to give Sri Lankan President Mahinda Rajapaksa a strong message about human rights abuses and supporting an independent inquiry into thousands of civilian deaths at the end of the civil war in 2009.
They also want him to break with convention to oppose Sri Lanka holding the chair of the Commonwealth for the next two years.
Mr Key supported a boycott of the Black Caps to Zimbabwe in 2009 on both safety grounds and on "moral grounds".
But he says there is no problem with the Black Caps playing Sri Lanka.
"There have been times we have expressed concerns about countries, Zimbabwe being one, but they've played in Sri Lanka for a long period of time," he said yesterday in Colombo.
"Hopefully they'll keep winning like they did earlier in the week."