"I have said it before. I urge everyone to sit together to discuss what would achieve the interests of our nation," Mursi said in an interview published in the state-owned Akhbar al-Youm newspaper.
The interview comes a day after tens of thousands of Mursi supporters massed in Cairo in a show of strength ahead of opposition protests planned for June 30.
Egypt is deeply polarised. Mursi's supporters say he is clearing institutions of decades of corruption but his critics accuse him of concentrating power in the hands of his Muslim Brotherhood movement.
There is much anticipation and anxiety ahead of the June 30 protests, with fears of violence and instability. But Mursi says there is still room to resolve differences off the streets.
He said he would consider bringing forward parliamentary elections, which are scheduled to take place later this year, although no date has yet been set.
"I will continue in my pursuit for contact, and I may speed up parliamentary elections as a way of involving everyone in an agreed method to manage our differences," Mursi said.