Shafiq, a former intelligence chief and Hosni Mubarak's last prime minister, faces Brotherhood's Mohammad Morsi in a two-way presidential contest on June 16, 17.
The presidential contest that started with a very close first round has polarised Egypt, as many people see Shafiq as a remnant of the regime they have done away with.
Muslim Brotherhood's Supreme Guide Mohamed Badie called on all Egyptians to vote in the presidential election run-off, and specifically appealed to Coptic Christians to consider national interest while casting their ballots.
"You are our dignified brothers, and reform of the homeland is reform for all citizens, Muslims and Christians, for we have both suffered from sectarian strife and the divisive practices of the former regime, which you undoubtedly do not want to bring back to power," Badie said, addressing Copts in a statement, without directly referring to Shafiq.
A large section of the Coptic vote in the first round is believed to have gone in favour of Shafiq, who some people look up to to bring back the stability of Mubarak's time.
Media reports have claimed that Copts voted for Shafiq during the first round upon instructions of the church. However, this was denied by Bishop Pachomius, the acting pope of Egyptian Copts.
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In an interview to Al-Arabiya last week, the Bishop said he would welcome an Islamist president provided he respects civil liberties and the rights of Copts.
He stressed that he did not support either candidate and was not calling on people to vote for one in particular. Christians constitute 10 per cent of the Egyptian population.
Badie, meanwhile, also appealed to the military and the police to protect the election in accordance with law, and to the judiciary to manage the election with utmost honesty.
"I urge citizens not to allow any attempt to falsify the will of the people," he concluded.