Public transport will be free in Victoria for a month and in Tasmania until July, in an effort to encourage people to switch from driving and to alleviate the surge in fuel demand.

However, the NSW and Western Australian governments will not follow suit, with NSW’s transport minister saying it needs to “keep our powder dry” to deal with a crisis that may last much longer than a month.

The Allan government announced on Sunday that it would make all metro and regional V/Line trams, trains and buses free from 31 March until the end of April.

The government said the free fares were a temporary measure, costing about $71m in forgone revenue

Also on Sunday morning, the Tasmanian premier, Jeremy Rockliff, announced buses and Derwent River ferries would be free across the state from 30 March until 1 July.

The state’s transport minister, Kerry Vincent, said the scheme would save commuters between $20 and $88 a week.

However, the NSW transport minister, John Graham, said on Sunday: “I want to be clear, the NSW government isn’t going down the path of free public transport for a couple of days, or for a month.

“This situation will last for more than a month. We need to keep our powder dry to be able to assist the broader economy.

“That’s the concern of the NSW government, we’re really planning to make sure that we can make it through this next period.”

Graham said he was not criticising other states for taking a different approach. The “millions of dollars” that the public paid each day for public transport would continue to be reinvested in the system and on improving reliability, he said.

The WA premier, Roger Cook, also rejected offering free public transport during the fuel crisis, saying the state’s fares were already at a “historically low” level comparable to “when Rick Astley was on top of the charts”.

The energy shock from the war in the Middle East has resulted in soaring prices of petrol and diesel, as well as fuel shortages in some parts of Australia.

In federal parliament, the ACT senator David Pocock and the Greens have been calling for free nationwide public transport during the fuel crisis.

But despite having to pay significantly more for fuel, Australians don’t appear to be driving less or taking public transport more – at least not yet, according to Guardian Australia’s analysis of usage data earlier this week.

During the free period in Victoria, the state government has promised all Myki gates will be open and passengers will not have to touch on. Those who do accidentally will not be charged, and if for some reason they are, they can get a refund.

Myki passes, including yearly passes, will automatically be paused and resume after April, the government said.

People travelling on V/Line coaches outside the Myki network will need to book a free ticket to secure their seat. However, people will not need a ticket to travel on trains outside the Myki network.

The public transport minister, Gabrielle Williams, said the government expected public transport to get busier but that it could meet the increase in demand.

“We expect to see increases in patronage across trains, buses and trams over the month ahead,” Williams said.

“This is why it’s so important that we’ve not only expanded our public transport network but also added thousands of services to it.”

The premier, Jacinta Allan, said she was determined to do everything within her control to help Victorians deal with rising fuel prices.

“This is a temporary measure to help with the cost of living – it will take pressure off the pump and help you save,” she said.

“This won’t solve every problem, but it’s an immediate step to help Victorians right now while we keep working on new solutions to make Victoria more affordable.”

Across Australia, weekly petrol bills have risen by $20 or more since the end of February for the average household using 35 litres of fuel.