Australia's big four banks have offered support including loan deferrals or waiving fees for customers under financial strain as a result of NSW's COVID-19 lockdown, amid warnings the cost to the economy could top $1 billion a week.

Commonwealth Bank chief executive Matt Comyn on Sunday urged customers who may be already financially affected by the lockdown or worried about the knock-on effects to contact their bank in order to find out what support could be tailored to them.