Francis also did not mention a recent military crackdown on the Rohingya - described by the UN as a textbook campaign of "ethnic cleansing" - as he delivered a speech to Burma's civilian leader Aung San Suu Kyi and other diplomats in the capital Naypyitaw.
But he lamented how Burma's people have suffered "and continue to suffer from civil conflict and hostilities", and insisted that everyone who calls Burma home deserves to have their basic human rights and dignity guaranteed.
Rohingya Muslims have faced state-supported discrimination in the predominantly Buddhist country for decades, deprived of citizenship and unable to access basic services such as education and health care.
In August, the army began what it called "clearance operations" in Rakhine state following an attack on police posts by Rohingya insurgents.
The violence, looting and burning of villages has forced more than 620,000 Rohingya to flee to Bangladesh.
In the most anticipated speech of his week-long trip to Burma and Bangladesh, Francis expressed support for Ms Suu Kyi's efforts to bring about reconciliation among different groups after decades of military dictatorship, and insisted that religious differences in must never be a cause for division or distrust.
"The future of Burma must be peace, a peace based on respect for the dignity and rights of each member of society, respect for each ethnic group and its identity, respect for the rule of law, and respect for a democratic order that enables each individual and every group - none excluded - to offer its legitimate contribution to the common good," he said.
His avoidance of the term "Rohingya" and his encouragement for Ms Suu Kyi's government disappointed activists and human rights groups who have criticised her for what they consider a weak response to the military crackdown.
Phil Robertson, deputy director of Human Rights Watch's
Asia division, said: "The Rohingya have been stripped of so many things but their name should never be one of them, and we hope that the Pope will use the word Rohingya in his Mass (on Wednesday)."
Kyaw Naing, a Rohingya Muslim who lives in a camp in Rakhine state, said: "We were very happy and hopeful on his visit. But since the Pope is not allowed to call out the name 'Rohingya', we wonder how bad the human rights situation is in Myanmar (Burma). He is the holiest man in the world but it's so sad to see that even the holiest man cannot call our identity."
The term "Rohingya" is shunned by many in Burma because the ethnic group is not a recognised minority in the country.
Ms Suu Kyi referred to the "situation in the Rakhine" in her speech to Francis in the huge conference centre in Naypyitaw, but used the conflict as an opportunity to thank those who have supported the government as it seeks to "address long-standing issues - social, economic and political - that have eroded trust and understanding, harmony and co-operation" in Rakhine.
She said the government's aim is to carry forward the peace process and strengthen Burma's diversity "by protecting rights, fostering tolerance, ensuring security for all".
Francis arrived in Naypyitaw after meeting leaders of Burma's different religious groups, and also a prominent but controversial Buddhist leader who has criticised the Rohingya.
The Pope stressed a message of "unity in diversity" in his 40-minute meeting with Buddhist, Hindu, Muslim, Christian and Jewish leaders and told them they should work together to rebuild the country, Vatican spokesman Greg Burke said.
Francis's meeting with Buddhist monk Sitagu Sayadaw was undertaken "in an effort to encourage peace and fraternal coexistence as the only way ahead", Mr Burke said.
