New Zealand's south island rocked by earthquake

New Zealand has been rocked by two earthquakes less than an hour apart.

Wellington was hit by a magnitude 5.0 tremor about 50 minutes after a 5.8 magnitude struck south-west of Invercargill.

There are no current tsunami warnings.

The first quake hit about 1.50pm local time at the southern end of the South Island.

It caused "moderate shaking," the New Zealand Herald reports.

While the quake was initially classified as strong, it has since been downgraded to moderate. 

It hit 585km south-west of Invercargill at a depth of 12km and might have been felt in Balclutha, Gore, Invercargill, Lumsden, Roxburgh, Te Anau and Tuatapere, GeoNet said.

The quake comes just hours after a powerful 7.1-magnitude earthquake struck Mexico, toppling buildings in the capital and sowing panic on the anniversary of a devastating 1985 quake.