The delegates insist that having a common understanding on what terrorism is would permit the United Nations and other world bodies to fight it jointly and help create laws that would allow for the perpetrators to be prosecuted.
The leaders argued on Thursday that political aims should never be used as an excuse to kill innocent civilians, in part because governments often use violence to accomplish goals.
The discussion came hours before UN Secretary-General Kofi Annan was to deliver a key policy speech before dozens of terrorism experts and former world leaders, who are supposed to offer recommendations on the issue.
The conference, which will conclude on Friday, was timed to commemorate the first anniversary of the Madrid train bombing, which killed 191 people and injured more than 1500.
The attacks on 11 March last year are believed to have been carried out by armed Islamist groups.
Financing terrorism is the other key issue on the agenda. Experts urged world leaders to create an international institution under the UN to track the elusive methods terrorists use to raise money.
The draft recommendation said measures undertaken so far to curb terrorist financing were insufficient to cut the flow of funds to al-Qaida and other international groups.
The experts stressed that governments need to be more flexible if they hope to turn off the tap.