PLO chief vows crackdown on violence
Abbas said he had had positive meetings with militant groups.
A steady stream of mourners pay their final respects.
After the opening prayer, funeral services begin for Yasser Arafat.
A look back at the life and political career of Yasser Arafat.
How the world viewed Yasser Arafat.
GAZA CITY (CNN) -- Palestine Liberation Organization chairman Mahmoud Abbas says officials will take steps to end lawlessness and violence in the Palestinian territories ahead of scheduled January 9 elections for president.
"This is a test for all the Palestinian people and the Palestinian leadership to prove to themselves and to the world that they can build a state," Abbas said in an interview with CNN Tuesday.
Abbas, a former prime minister who has been mentioned as a possible candidate in the elections, said any show of illegal arms in the streets would not be tolerated and Palestinian officials would do what they could to enforce order.
The long-time Palestinian politician, who is popularly known as Abu Mazen, said he had had positive meetings with militant groups such as Hamas, Islamic Jihad and the Popular Front for the Liberation of Palestine.
He said he asked them to help calm down the situation in the territories in order to give the Palestinians time to regroup.
Abbas said he did not know whether he would run for the post of Palestinian Authority president. That is up to the Fatah Central Committee, he said.
Abbas said the first priority was to unify Fatah, which had been headed by the late president Yasser Arafat, who died last week. Then, he would work out agreements with the opposition groups.
Eventually, the Palestinians would be ready to work with Israel, he said. So far, there have been no contacts with Israel, but Abbas said Palestinians must be ready for the Israeli disengagement plan if and when it happens.
Some analysts have said Abbas would be the most effective politician to work for Palestinian nationhood and peace with Israel.
But Abbas, who escaped injury Sunday in a Gaza gunfight, said Palestinians also want to unify competing security services. It is a reform Arafat promised but never delivered.
State Department deputy spokesman J. Adam Ereli said Wednesday that Secretary of State Colin Powell would be visiting Palestinian leadership early next week.
He called it "an opportunity for us to discuss with them their plans for elections, their plans for moving forward, engaging with Israel, and how all of us can support the essential step of helping a new Palestinian leadership emerge, a leadership that is committed to democratic reforms, transparency, the rule of law and fighting terror."
Powell will also meet with Israeli leaders "and explore ways that we can support the Palestinian leadership" and pursue an "orderly withdrawal" from Gaza.
CNN Producer Sausan Ghosheh contributed to this report