* Recommendation made in internal military discussions
* U.S. left 700 troops behind in Jordan after drills
* Lebanon, Iraq dragged into Syrian conflict, violence grows
The top U.S. military officer said on Wednesday he has recommended bolstering Lebanese forces grappling with the fallout from Syria's civil war by sending in military trainers and accelerating arms sales.
General Martin Dempsey also said he had recommended helping Iraq better deal with the re-emergence of al Qaeda.
"We've made a recommendation that as we look at the challenges faced by the Lebanese armed forces, the Iraqi security forces with a re-emerging al Qaeda in Iraq, and the Jordanians, that we would work with them to help them build additional capability," Dempsey told reporters at the Pentagon.
A spokesman said Dempsey's recommendations were made "in recent weeks" during internal discussions with the U.S. military's Central Command, as it deliberates how to respond to the growing, regional unrest.
After two years of fighting that has killed more than 100,000 people, Syria's war is dragging its neighbors into a deadly proxy confrontation between Shi'ite Iran supporting President Bashar al-Assad and Sunni Arab Gulf nations backing the Syrian rebels.
Both Iraq and Lebanon have suffered increasing violence at home as the Syrian conflict has escalated.
Dempsey was nominated by President Barack Obama on Wednesday for another two years as chairman of the Joint Chiefs of Staff.
He was responding to a question at the news conference about whether Lebanon had asked for military help and whether the U.S. military might go into that country.
"When you say would we send the United States Army or the United States military into Lebanon, I'm talking about teams of trainers, and I'm talking about accelerating foreign military sales for equipment for them," Dempsey said in response.
"This is about building their capability, not ours."
A spokesman clarified that this would come on top of any ongoing U.S. military support being provided to Lebanon and Iraq.
The United States has left about 700 U.S. combat-equipped troops in Jordan after a military drill, which also fears a spillover of the war into its territory and where an estimated half-million Syrian refugees have fled to escape the bloodshed.
RISKS OF NO-FLY ZONE
The Pentagon has also announced that it would leave Patriot missiles and F-16 fighters in Jordan after the same drill, fueling speculation that the United States might be considering a no-fly zone that would prevent the Syrian military from flying its aircraft.
Although Obama has not ruled out participating in a no-fly zone, he has appeared skeptical about such a move, and his military commanders, including Dempsey, have been outspoken about the risks involved.
Dempsey, suggesting a no-fly zone may do little to stem the bloodshed, told reporters that Assad's air power was responsible for few of the casualties.
"And if we choose to conduct a no-fly zone, it's essentially an act of war, and I'd like to understand the plan to make peace before we start a war," Dempsey said.
He also noted that any U.S. decision to impose a no-fly zone in Syria would require tough decisions about America's military priorities at a time of shrinking budgets and other demanding commitments - including the Afghan war.
"We are suffering some readiness shortfalls right now," Dempsey said. "We have resources that are at heightened states of alert in the vicinity of the Korean peninsula, in the Gulf, because of potential provocations (by) Iran. Clearly, we still remain very deeply engaged in Afghanistan.
He added: "And the question for the nation will be - and for our elected leaders - where will we prioritize our resources? But if that (a no-fly zone) becomes a priority, we can make it happen."