Palestinians and Israelis, Abbas said, are destined to live side by side.
But he said any cease-fire must be mutual.
Referring to the most recent bloodshed, Abbas deplored violence from either side. "We condemn these [violent] actions, whether by the Israeli occupation forces or the reactions of some Palestinian factions," he said, noting that such moves cannot provide "the calm needed to enable a credible, serious peace process." Abbas added, "We are seeking a mutual cease-fire to end this vicious circle."
Abbas's election on 9 January raised hopes for a fresh boost to peace efforts.
He has said he wants to end the four-year armed uprising against Israel and rein in militant groups.
But today's ceremony in Ramallah was overshadowed by the latest violence and the responses to it.
In an attack on 13 January, Palestinian militants killed six Israelis at a Gaza crossing point.
In response, Israeli Prime Minister Ariel Sharon announced his decision to cut ties with Abbas and the Palestinian Authority.
That Israeli decision was criticized earlier today by the man whom Abbas wants to stay on as Palestinian prime minister, Ahmed Qurei.
"This is a wrong decision and reflects that Israel is trying to find any excuse to disrupt any serious effort that leads to reviving the peace process and to achieve calm," Qurei said. "This is a wrong decision."
In his speech, Abbas condemned the Gaza attack.
But even as he spoke, there was fresh violence. Six Palestinians were killed by Israeli Army fire in two separate incidents in Gaza.
A further sign of the difficulties ahead came from the militant group Hamas. Its spokesman, Sami Abu Zhuri, said a cease-fire could only be considered if Israel "stops all kinds of aggression" against Palestinians.
(with wire and RFE/RL reports)