Mr Powell says the US wants "specific action" from Syria
US Secretary of State Colin Powell has called on Syria and Lebanon to end all support for groups Washington classifies as terrorist organisations.
Speaking after talks in Damascus and Beirut, Mr Powell said he had made it clear to the Syrian and Lebanese leaders that there was a "new strategic situation" following the fall of Saddam Hussein in Iraq and the publication of a new peace plan for Israel and the Palestinians.
He said Syria had already closed the offices of some anti-Israel groups in Damascus but he expected Syria "to do more".
The Syrian Arab News Agency (Sana) said the talks between Syrian President Bashar al-Assad and Mr Powell had been "constructive, candid and positive".
Earlier, Syrian Foreign Minister Farouq al-Sharaa said Syria would listen to Mr Powell but would not respond to any ultimatums.
Action on Hezbollah
Mr Powell told reporters in Beirut on the final stage of his four-nation trip that Mr Assad had said only that the points he raised would be considered.
The BBC's Lyse Doucet says Mr Powell adopted a tough tone and made it clear that the US expects Syria and Lebanon to comply with Washington's plans for the region.
It is time for the Lebanese army to deploy to the border and end the armed Hezbollah militia presence
The secretary of state urged Lebanon to stop the activities of Hezbollah guerrillas on the border with Israel and he called on Syria to end its support for the Iranian-backed movement.
"It is time we believe for the Lebanese army to deploy to the border and end the armed Hezbollah militia presence," he said.
But while the offices of some anti-Israeli militants in Damascus have been shut, our correspondent warns that Syria may be less amenable to demands over Hezbollah which it considers legitimate.
Mr Powell said there were opportunities to resolve long-standing issues - such as Syrian troops in Lebanon and Israel's capture from Syria of the Golan Heights - but all sides had to take action.
The US also want Syria to crack down on the presence in Damascus of groups such as Hamas and Islamic Jihad which launch attacks on Israel.
After his talks with Mr Assad, Mr Powell said the US "will be watching [Syria] very carefully and [will be] anxious to engage with Syria on various performance measures as we go forward."
Relations between Washington and Damascus deteriorated last month as the US accused Syria of trying to undermine it during the war in Iraq.
Mr Powell stressed there were no plans for any military action against Syria.
But in his weekly radio address, US President George W Bush made what correspondents say was another warning to countries like Syria and North Korea who are accused by Washington of aiding terrorists or developing weapons of mass destruction.
"Our government has taken unprecedented measures to defend our homeland and, more importantly, we will continue to hunt the enemy down before he can strike," Mr Bush said.