Opposition Leader Bill Shorten has taken a swipe at US presidential candidate Ted Cruz for claiming the rates of sexual assault and rape soared in Australia following the introduction of strict gun laws.

Mr Shorten has written directly to Senator Cruz after the conservative Christian – who is billionaire Donald Trump's closest rival for the Republican nomination – made the claims about the post-Port Arthur massacre laws earlier this month.

"As you know, Hugh, after Australia did that [gun buyback program], the rate of sexual assaults, the rate of rapes, went up significantly, because women were unable to defend themselves," he said on high-profile radio host Hugh Hewitt's show.