Powell was heading Friday evening to the Syrian capital of Damascus for "a rather full and candid conversation" with Assad and Foreign Minister Farouk al-Sharaa.
En route to Damascus, Powell stopped in Albania to meet with President Alfred Moisiu and Prime Minister Fatos Nano and sign a pair of agreements. One was a U.S.-Albanian accord designed to spare U.S. soldiers who take part in peacekeeping activities from being prosecuted by an international criminal court. Albania is the 32nd country to strike such a one-on-one agreement with the United States.
Powell also signed a charter in support of efforts by Albania, Croatia and Macedonia to integrate fully into Europe. Powell said he hopes the agreement will help "move these countries in the direction of eventual membership in NATO and the European Union."
Between meetings, Powell walked through downtown Tirana and shook hands with a crowd near a local park.
The talks in Damascus are a prelude to a second Mideast trip by Powell next week for meetings with Israeli Prime Minister Ariel Sharon and Mahmoud Abbas, the new Palestinian prime minister.
The Damascus meetings were taking place amid renewed prospects for Israelis and Palestinians to resolve their bloody 31 months of fighting.
Powell was expected to raise concerns over the fact that Syria allowed wanted Iraqi leaders to cross its border and hide out. He also planned to call attention to the offices kept in Syria by several Palestinian factions, including the militant Islamic Hamas and Islamic Jihad, which the Bush administration has classified as terrorist organizations.
"We will speak candidly about some of the disagreements we had with Syria in recent weeks, as the war was being conducted and concluded," Powell said Thursday.
"They are going to have a new and different kind of neighbor than the neighbor they had for the last 20-odd years…I will encourage them to review these changes, and take a look at some of their past policies, and see whether those policies seem to be relevant in light of a new, changed situation."
The Syrians have denied that planning for anti-Israel attacks takes place in the Damascus offices. But Powell will expect the Syrians to make clear to the groups that if they cross the line they will be expelled.
CBS News Correspondent Robert Berger in Jerusalem reports Israel sees Powell's plan to confront Syria about terrorist support as a big step forward. Israel has long complained that terrorist groups often receive orders for suicide bombings from their leaders based in Damascus.
"Many Israelis were surprised to discover Syria being accepted as a legitimate member of the U.N. Security Council, knowing that Syria is the home for many headquarters of terror organizations," said Israeli analyst Alon Ben David.
Also on Powell's list is the Lebanese Hezbollah guerrilla group, which led the fight against Israel's occupation of a strip in south Lebanon. The Israelis pulled out in May 2000.
Powell wants Syrian support for the peace process and for the newly formed Palestinian government.
Opening his three-day trip, Powell said Thursday that much work remains before President Bush's goal of a Palestinian state by 2005 can be met. That work includes ending suicide bomb attacks and harsh defensive actions by Israel, he said.
"We have got to get beyond this period of suicide bombings and retaliatory actions, or other defensive actions that are taken," Powell said.
A road map, or blueprint, for negotiations between the two sides was announced Wednesday. It calls for establishment of a Palestinian state within three years, an end to violence by both the Palestinians and Israel, an immediate cease-fire and the dismantling of some Israeli settlements — along with a freeze on new construction.
"There is a significant difference now," Powell told Spanish Television TVE. "And that is that the Palestinian Authority has begun to transform itself."
Abbas, Powell said, "has independent authority, not just authority from Arafat." While Abbas immediately condemned violence and said "we must end the terror," Arafat is a failed leader, Powell said.
Still, Powell said there were groups in the Palestinian Authority that do not want to see progress.
The proposal's announcement was followed closely by a bomb attack in Tel Aviv that killed three, and an Israeli crackdown on a Hamas stronghold in which 12 Palestinians died.
Powell urged Sharon and Abbas, also known as Abu Mazen, to work with the United States and other international partners "to find the peaceful way forward, even when faced with these kinds of tragic scenes that we have seen in recent days."
Powell spoke after meeting with Spanish Foreign Minister Ana Palacio in Madrid — the place where the road map began taking shape a year ago among the United States, the European Union, the United Nations and Russia.