Labor pledged at the 2019 and 2022 federal elections to end the trade, but the government has consistently said it won't happen this term to allow the industry a smooth transition.
The 23 groups, including the Australian Livestock Exporters' Council, National Farmers Federation, Grain Producers and Northern Territory Cattlemen's Association, want Mr Albanese to reverse his government's policy.
"Middle Eastern countries reliant on Australian live sheep exports are critical to diversify Australia's trading partnerships," the letter states.
"The phase out policy will jeopardise trade deals Australia is pursuing in the region and will erode our reputation as a reliable economic partner."
The signatories said there had been a 20-fold increase in two-way investment in the past 20 years.
Labor made the commitment to abandon live sheep exports after 2400 sheep died of heat stress in 2017, while travelling on a ship from Australia to the Middle East.
But the stakeholders argue Middle Eastern markets will turn to other countries that don't have the same animal welfare standards of Australia.
"If the decision is being made on the grounds of improving animal welfare, the ban will be an abject failure."
The letter also links the policy to recent dramatic falls in sheep prices across Australia.
"Domestically the fallout associated with the policy announcement is already occurring with a devastating collapse in producer confidence and the sheep industry - not just in Western Australia, but nationally."
The letter to the prime minister follows a similar plea to Agriculture Minister Murray Watt in March, advising the phase out was a "red line" issue for the entire sector.
"This letter was a request for your Government to listen - but we have not been heard."
The federal government says it remains committed to the phase out.
"The Albanese government has been clear that we intend to implement the election commitment to phase out live sheep exports, but that it will be done in an orderly way, in consultation with industry and other stakeholders through the independent panel," a spokesman said.
The government is awaiting a report from an independent panel set up to deliver the transition.
It was meant to report its findings in September, but was granted an extension to October 25.
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