"I appeal to our citizens and residents for a week of silence, peace and calm as we pay respect to this one person whom our country owes so much," Marape said. "He is universally loved in our country, may his memory bind out nation still."
Cabinet will meet later Friday to announce details of a state funeral for the leader who was also known as Papua New Guinea's Grand Chief and Father of the Nation.
Police Commissioner David Manning said police would ensure that Papua New Guineans mourn peacefully and that "opportunists do not take this sad day in our history to create fear and panic."
Political differences can lead to violence in Papua New Guinea where elections are often accompanied by riots.
"Grand Chief Sir Michael believed in the unity of this nation of a thousand tribes and gave his life to this cause," Manning said. "He stood up when it mattered against the colonial masters and a world filled with racism, ignorance and hatred and dedicated his life to bring about a united and independent nation."
Somare was born on April 9, 1936, in the city of Rabaul in East New Britain, which was occupied by Japan during World War II. His earliest education was in a Japanese-run school in the village of Karau where he learned to read and write in Japanese.
He was raised the son of a police officer in the province of East Sepik, which he went on to represent in Parliament. Ron May, emeritus fellow at the Australian National University's Department of Pacific Affairs and a Papua New Guinea expert, said Somare was one of the Pacific's most prominent and respected leaders.
"Papua New Guinea made a smooth transition to independence in 1975, with Somare as prime minister, confounding those in Australia and elsewhere who had predicted political and economic collapse," May recently wrote.
"It remains one of a fairly small number of post-colonial states that have maintained an unbroken record of democracy."
New Zealand Prime Minister Jacinda Ardern said Somare had been an "influential figure" during a "remarkable five decades" in Parliament.
"He is widely respected as Papua New Guinea's 'Papa blo Kantri' - Father of the Nation - and had a leadership role as a statesman of the Pacific," Ardern said. "He will be deeply missed."
Australian Prime Minister Scott Morrison said Somare was a "towering figure in the history of Papua New Guinea".
"As a driving force in the development of Papua New Guinea's national constitution, and the nation's first and longest-serving prime minister, Sir Michael has an unparalleled place in the history of Papua New Guinea," Morrison said.
On the 30th anniversary of Papuan New Guinea's independence, Somare said he was generally pleased with his country's progress.
"I'm happy about the way things have gone but, you know, we could have done better," he told Australian's SBS network in 2005.
His last term as prime minister ended controversially in 2011 while he was in a Singapore hospital. Lawmaker Peter O'Neill successfully moved a motion in Parliament that the post of the prime minister was vacant.
O'Neill was elected premier and clung to power despite the Supreme Court twice ruling against him until he was legitimately elected in 2012.
Somare is survived by his wife Veronica and children Bertha, Sana, Arthur, Michael and Dulciana.
