"We have learned from the past 10 years, however, that it is not enough to simply alter the balance of military power without careful consideration of what is necessary in order to preserve a functioning state," he said.
The US announced in June it would provide military support to vetted groups of rebels, and this week Administration officials said it had overcome concerns from Congress over how to safeguard against weapons falling into the hands of Islamist militants. "Should the regime's institutions collapse in the absence of a viable opposition, we could inadvertently empower extremists or unleash the very chemical weapons we seek to control," he warned.
Dempsey advocated an approach that drew in US allies in the region. He concluded by supporting the current position of the Obama Administration, which has long been reluctant to deepen involvement in Syria.
"We should help develop a moderate opposition - including their military capabilities - while maintaining pressure on the Assad regime."
Hundreds of men who took up arms against President Bashar al-Assad are defecting back to the government side.
Disillusioned by the Islamist twist that the "revolution" in Syria has taken, exhausted after more than two years of conflict and feeling that they are losing, growing numbers of rebels are signing up to a negotiated amnesty offered by the Assad regime.
At the same time, the families of retreating fighters have begun quietly moving back to government-controlled territory, seen as a safer place to live as the regime continues its intense military push against rebel-held areas.
The move is a sign of the growing confidence of the regime, which has established a so-called "ministry of reconciliation" with the task of easing the way for former opponents to return to the government side.
Ali Haider, the minister in charge, said: "Our message is, 'if you really want to defend the Syrian people, put down your weapons and come and defend Syria in the right way, through dialogue'."
Haider, who has a reputation as a moderate within the regime, has established a system in which opposition fighters give up their weapons in exchange for safe passage to government-held areas. Rebel fighters have privately said that they are aware of the amnesty offer, and that some men had chosen to accept it, although they say that the numbers involved remain a small proportion of those fighting the Government.
"I used to fight for revolution, but now I think we have lost what we were fighting for," said Mohammed, a moderate Muslim rebel from the northern town of Raqqa who declined to give his last name. "Now extremists control my town. My family has moved back to the Government side because our town is too unsafe. Assad is terrible, but the alternative is worse."
The prevalence of extremist Islamist groups has caused some opposition fighters to "give up".
Assad 'won't lose power'
Syrian President Bashar al-Assad is not going to lose power unless there is foreign intervention amounting to a full-scale war, according to a top Middle-East politician.
The Iraqi Foreign Minister, Hoshyar Zebari, said with a united army in control of Damascus and the major Syrian cities, Assad "will survive for the foreseeable future". Zebari is one of the few leaders to be in touch with all parties in the Syrian civil war, including the Government, the opposition and their foreign backers.
He expressed pessimism about peace negotiations in Geneva proposed by the US and Russia, but said he believes that the best way forward may be a ceasefire policed by the UN before any agreement on a transitional government. He said: "I think it would be possible to do that with strong engagement by the UN to follow through and maybe some international peacekeepers."
He was scornful of recent speculation about the possibility of a military coup displacing Assad.
He said "the idea of the army moving is a recent invention", adding that it reminded him of abortive attempts by the CIA to organise the overthrow of Saddam Hussein in the 1990s, but that "this kind of regime is coup-proof".
Zebari said he believes that the stalemate would not be broken even if the Government or the rebels captured a few towns. "I saw lots of people but it is very depressing," he said of recent meetings in the Middle East and Europe with all those involved in Syria, adding: "Nobody has any idea how to help."
- additional reporting Independent