As aftershocks continue to rattle the country, a petition has been launched urging funding for round-the-clock staff at earthquake monitoring service GeoNet.

READ MORE: Damage growing in Wellington with each aftershock

The biggest aftershocks overnight have been magnitude 3.9. One was south-east of Kaikoura just after midnight, and another south-west of the town at just after 4am.

The petition has been started by the Labour Party, whose Civil Defence spokesperson Clare Curran insists that last Monday's 7.8 earthquake raised serious issues in the monitoring and alert system.

"I hear myself from tsunami experts...the problem is that people are being woken up from sleep and asked to analyse complex information and make a decision very quickly," Curran said.

"The matter is quite clearly urgent. Last week's large quake and the resulting tsunami alert indicated that there is a critical need for analysis to be done 24/7," she said.

Prime Minister John Key yesterday announced a mobile warning system could be on its way, however Clare Curran said the government hasn't done anything to solve monitoring problems since the Christchurch earthquakes in 2010 and 2011.

"What have they been doing in the last three years?" Curran asked.

"They've spent [$538,000] in the last two years on investing in a solution which is now sitting on a shelf [and] now they're going ahead and looking at another service."

The petition currently has over 10,000 signatures.

Ships from foreign navies which have been helping out in Kaikoura post-quake will visit Wellington today.

The USS Sampson, HMAS Darwin and HMCS Vancouver will enter Wellington Harbour at about 8am this morning.

The New Zealand frigate Te Kaha and tanker Endeavour will also be there, while Canterbury ferries evacuees from Kaikoura to Lyttelton.

The ships are expected to leave for Auckland this afternoon.