US Secretary of Defence Leon Panetta and Jordan's King Abdullah II on Thursday discussed the question of a political transition in "a post-Bashar al-Assad Syria," Pentagon spokesman George Little said.
"They talked not only about how to deal with the current crisis that is being fuelled by the intolerable acts of the regime, but also the prospects for political transition in a post-Bashar al-Assad Syria," Little told reporters.
"They agreed that strong international pressure needs to be sustained to make it clear that Assad must go, and that the Syrian people deserve to determine their own future."
Panetta pledged that "the United States will work with Jordan to explore ways to continue to provide humanitarian aid to those affected by violence in Syria," Little said.
The US defence secretary was in Jordan on the last leg of a regional tour of Tunisia, Egypt and Israel.
"Both of our nations share concerns about what is happening in Syria and the impact that that could have on regional stability," Panetta told reporters before arriving in Amman.
"We are working very closely with them (the Jordanians) along with a lot of international and non-governmental partners, to provide humanitarian assistance to support those that have been affected by violence in Syria."
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The Zaatari camp in Mafraq can take up to 120,000 people.
More than 276,000 Syrians have fled their country, mainly to Jordan, Turkey and Lebanon, according to the UN refugee agency UNHCR.
"The department of defence has reached unprecedented levels of cooperation with the Jordanian armed forces. We have done that in light of what is happening in Syria," Panetta said.
"We have done that in a way to try to develop as close a partnership as possible to deal with any contingency that may happen there."
The king on Wednesday visited the border village of Tal Shehab, where he and Jordanian troops had the iftar meal to break the Ramadan fast, the palace said.
"At dawn, 600 Syrians came under Syrian army fire as they fled to Jordan. The Jordanian army responded and allowed them to cross," said Zayed Hammad, head of the Ketab and Sunna Society which cares for thousands of Syrians who have fled the violence.
"Nobody was hurt. This happens all the time, but this morning's fire exchange took longer than usual."
Syrian troops opened fire last Thursday on a group of civilians fleeing into Jordan, killing a three-year-old child.
The conflict in Syria has killed more than 20,000 people since the uprising against the Assad's regime erupted in March 2011, the Syrian Observatory for Human Rights says.