It would allow hazards to be detected more quickly, and people could be warned through an app, similar to the one Geonet already uses.
Gledhill said it would be most useful for warning large coastal populations about a tsunami triggered from offshore faultlines such as the Kermadec Trench.
But it could also be applied to quakes, volcanoes and other hazards.
Civil Defence Minister Gerry Brownlee would not rule a change to the monitoring system today, saying he wanted to discuss the matter with Geonet's owner GNS Science.
But it was "not something we will be doing in the next 24 hours", he said.
Labour leader Andrew Little backed the call for an upgraded monitoring system, saying a country built on multiple faultlines needed a full-time agency.
The absence of a 24-hour system appeared to have contributed to "confusing messages" about a potential tsunami following Monday's quake, he said.
The Labour leader lives near the coast in Wellington's Island Bay, and said he only became aware of a potential tsunami because of radio coverage of warnings in Christchurch.
Gledhill noted in his blog that even a full-time monitoring centre might not have been quick enough for the Kaikoura population on Monday.
"The best advice is still: if you are at the coast, and feel a long or strong earthquake, be gone"
"We were lucky the tsunami struck at low tide; high tide could have left more damage than I feel comfortable thinking about."