Mr Albanese landed in Singapore on Thursday night ahead of formal talks with Lawrence Wong on Friday during a brief visit to the city-state.
Singapore is the largest supplier of refined petrol to Australia, with the prime minister seeking to ensure a deal that would continue supply as global oil markets are hit by the conflict in the Middle East and the closure of the Strait of Hormuz.
"This is an important relationship at a time where fuel security is on the agenda, right around the globe due to the conflict in the Middle East. This relationship is more important than ever," he told reporters in Singapore.
"We know that it is in both of our countries' interests to engage with each other to make sure that we are both reliable suppliers, and our word means something."
"We have each other's word and indeed we have each other's back at this time."
Singapore provides 55 per cent of Australia's refined petrol and 26 per cent of all refined fuels entering the country.
Australia is also Singapore's second-largest supplier of LNG, responsible for nearly one-third of its total gas supply.
"Australia and Singapore are strategically aligned. We share values and we share a relationship of trust between each other. And that is why it's so important that at difficult times in the world we can rely upon each other," Mr Albanese said.
Mr Albanese will also visit Singapore's Jurong Island, where the city-state has three oil refineries, ahead of his formal bilateral meeting with Mr Wong.
Production at the facilities has been limited as most of the oil processed there comes via the Strait of Hormuz.
The prime minister said the visit to Singapore, which was organised on short notice, reinforced the ties between the two countries.
Singapore is Australia's largest two-way trade partner in Southeast Asia.
In March, Mr Albanese and Mr Wong signed a joint statement reaffirming Australia and Singapore's commitments to continue trading in energy.
The statement said the countries would "support the flow of essential goods including petroleum oils, such as diesel, and liquefied natural gas".
Acting Prime Minister Richard Marles said Australia was working with other countries in the region to ensure fuel would flow.
"We are working with our partners in East Asia around securing Australia's fuel supply ... and the prime minister's visit to Singapore is very much in that effort," he told ABC Radio.
