Friction has worsened since President Hosni Mubarak, who suppressed Islamists, was ousted last year. Since then Shenouda, who died on Saturday aged 88, often called for harmony and regularly met Muslim and other leaders.
Christians, who comprise about a tenth of Egypt's 80 million people, have long complained of discrimination and in the past year stepped up protests, which included calls for new rules that would make it as easy to build a church as a mosque.
Shenouda had served as the 117th Pope of Alexandria since November 1971, leading the Orthodox community who make up most of Egypt's Christians. His funeral will be held on Tuesday, Egyptian state media reported.
US President Barack Obama offered his condolences and Pope Benedict, leader of the world's Roman Catholics, offered prayers after being informed of his death.
Thousands of Christians queued in Cairo's Abbasiya district overnight and on Sunday morning at the cathedral where Shenouda's body was initially laid in a coffin and later seated on a ceremonial throne wearing gold and red embroidered religious vestments, a golden mitre on his head and holding a gold-topped staff.
He was popular among many of Egypt's Christians even outside the Orthodox Church, as well as among many Muslims. However, some Christian activists said Shenouda should have pushed the state harder to secure more rights for Christians.
In one phrase Shenouda often repeated and which was also cited in newspapers on Sunday, he would say: "Egypt is not a nation we live in, rather it is a nation that lives in us."
The burial is expected to take place at the Wadi el Natrun monastery in the desert northwest of Cairo, where the late pope had requested he be buried.
Shenouda was banished to Wadi el Natrun monastery in 1981 by then-President Anwar Sadat after he criticized the government's handling of an Islamic insurgency in the 1970s and Egypt's 1979 peace treaty with Israel.
Under Mubarak's rule, relations between the government and the Coptic church were generally smooth, with the pope portrayed in state media as a symbol of religious harmony, despite occasional outbreaks of sectarian violence.Religious dialogue
"We will remember Pope Shenouda III as a man of deep faith, a leader of a great faith, and an advocate for unity and reconciliation," the US president said in a statement issued by the White House.
Obama said Shenouda had been committed to national unity and was "a beloved leader of Egypt's Coptic Christians and an advocate for tolerance and religious dialogue."
Shenouda publicly supported Mubarak during his last days and before Mubarak's ouster by a popular uprising on Feb. 2011, a move that drew some criticism from some members of his church who joined the protests that ousted the president.
Some Muslim leaders also backed Mubarak in his last days.
Christians have long complained about rules that put more restrictions on building a church than a mosque and also say they have been discriminated against in the workplace.
Christians have accused hardline Islamists of attacking churches and said the authorities have failed to step in to protect them, although experts say some recent incidents have been fueled by local grudges as well as sectarian tensions.
Such violence has for years been sparked by disputes ranging from rows over church building to inter-faith romances.
The head of Egypt's ruling military council, Field Marshal Mohamed Hussein Tantawi, granted Christians working in state institutions three days mourning, state media reported.
Bishop Bakhomious, head of the church of Bahaira, a district in the Nile Delta north of Cairo, will temporally hold the post of pope for two months until a new leader is elected.
Egyptian media described the procedure for choosing a new pope as one based on a system of voting by board members of the church's city councils. The councils vote on three preferred candidates, and the final choice is made when a name is picked out of a box by a young child, the media said.
CAIRO (Reuters) -- Christians gathered on Sunday to pay final respects to Pope Shenouda III, who sought to soothe sectarian tension in his four decades atop Egypt's Orthodox Church but saw increasing flareups in the majority Muslim nation in the last months of his life.