Abbas said he and his Fatah delegation had told all their supporters that "we will not leave this holy place until we have agreed on everything good, with God's blessing".
"I tell our people to expect good news, and I hope this [meeting] will not be mere words in the air," Abbas said.
"It is pitiful to witness the bloody scenes in Gaza between the brothers"
Referring to the gun fights that killed more than 30 people in the past seven days, Meshaal turned to Abbas and said they both had to tell their supporters to respect the truce that took effect on Sunday.
"We want to give a message to the nation, and the world, to create a positive atmosphere for these talks," Meshaal said.
Ismail Haniya, the Palestinian prime minister, who heads the Hamas-led government in the Palestinian territories, added his voice to the spirit of goodwill.
"We ask God to grant that this will be a new page in Palestinian-Palestinian relations," he said.
Both delegations thanked Abdullah bin Abdul Aziz Al Saud, the Saudi monarch, for convening the talks, which come after months of failed negotiations between Fatah and Hamas and bloody street battles in Gaza and the West Bank that have killed scores of people.
The king did not attend the ceremony, but his hosting the negotiations and his choice of venue, a palace overlooking the Kaaba, a sacred sanctuary for Muslims, show the Saudis' strong desire to produce a breakthrough in the Palestinian conflict, which Arabs have long accused their leaders of neglecting.
After the inaugural speeches, the media were asked to leave the palace and the meeting was turned into a closed-door session.