"To all those who love Egypt, to the opposition, those who love this country and care for its interests, let's proceed together... help each other, love each other more... and move forward," said Morsi.
The Islamist president was speaking after a ceremony to mark the release of seven security personnel kidnapped last week in the lawless Sinai peninsula.
"Let's look forward, not back. Let's reconcile with those who seek reconciliation... I call on everyone to sit down together and dialogue, even if we disagree on points of view," he said.
Morsi, who hails from the powerful Muslim Brotherhood, is Egypt's first elected president since the 2011 uprising that toppled his predecessor Hosni Mubarak, himself in power for 30 years.
But his opponents accuse him of placing the interests of his Islamist movement above those of the nation, despite repeated vows to be a "president for all Egyptians".
His tenure has been marked by deep political polarisation, violent unrest and a crippling economic crisis.
Earlier this month, a campaign calling for his ouster gathered over two million signatures, its organisers said, including from high profile activists and celebrities.
The "Tamarod" (Rebellion in Arabic) campaign seeks to withdraw confidence from the Islamist leader because he has failed the revolution that brought him to power, they said.
"Because security has not returned, because the poor have no place, because I have no dignity in my own country... we don't want you anymore," the text reads.
"The campaign was launched because the president is no longer able to manage the country," Tamarod spokesman Mahmud Badr recently told AFP.
Tamarod has called for a mass protest outside the presidential palace on June 30 when Morsi marks one year in power.
But Morsi urged people to return to the spirit of the 2011 revolution which saw Islamists and secularists, men and women, standing together in an electrifying show of unity to bring Mubarak down.
"I reach out to everyone, to all those who wish this nation well, to really be the children of the January 25 revolution," Morsi said.
"Egyptians after January 25 are one people," he insisted.