Kerry is visiting the Middle East to press regional leaders to tackle the threat from Islamist militants in both conflicts - a task given greater urgency by the situation in Iraq, where ISIS, the Islamic State in Iraq and the Levant, has captured a series of towns and cities.
"We have even more to talk about in terms of the moderate opposition in Syria, which has the ability to be a very important player in pushing back against ISIS's presence," Kerry told Jarba in a meeting at Jeddah airport at the start of a brief trip to Saudi Arabia.
"President Jarba represents a tribe that reaches right into Iraq. He knows people there, and his point of view and that of the Syrian opposition will be very important going forward," said Kerry before a scheduled meeting with Saudi King Abdullah.
The Obama administration on Thursday asked for $500 million from Congress to train and equip vetted members of Syria's opposition, the most significant U.S. move so far to support those fighting against President Bashar al-Assad.
Saudi Arabia has been the most prominent backer of the Syrian rebels, and was very critical of Washington last year when it backed away from air strikes against Assad after a poison gas attack in Damascus.
Jarba told Kerry that the worsening situation meant more effort would be needed by both Washington and Riyadh, as well as others, to address the situation in Iraq, whose border with Syria he said was now "practically open". "The policies of Iraqi Prime Minister Nuri al-Maliki after eight years in power have resulted in greater division. Now the situation is very grave," he said.
Maliki, a Shi'ite Muslim, is a close ally of Sunni Saudi Arabia's main regional foe Iran, and is fighting to stay in power after coming under criticism over the ISIS-led advance.Washington has placed its hopes in forming a new, more inclusive government in Baghdad that would undermine the insurgency. In Baghdad on Monday, Kerry said Maliki assured him the new parliament, elected two months ago, would meet a July 1 deadline to start forming a new government.
Saudi Arabia has long distrusted Maliki as being too close to Iran and sees him as ruling on behalf of Iraqi Shi'ites to the exclusion of Sunnis. Last week Saudi officials, in an apparent message to Tehran, warned that foreign countries should stay out of Iraq.
Baghdad is racing against time as the insurgents consolidate their grip on predominantly Sunni provinces, and Kerry has been pushing Saudi Arabia to use its influence among fellow Sunnis in Iraq to join the government and ensure it represents everyone.
On Thursday King Abdullah ordered "all measures" to be taken to protect Saudi Arabia against militants.
Kerry met the monarch at his palace in Jeddah, where the U.S. delegation was ushered into the large marble-columned lobby of the palace. The king, who is over 90, spoke clearly in Arabic but did not get up when Kerry entered the large room.
On Thursday, Kerry met with foreign ministers from Saudi Arabia, Jordan and United Arab Emirates to inform them of plans for air strikes against ISIS once a new government is formed.
The United States also wants these countries to do more to cut off the flow of funding from private donors to ISIS.