Gen Selim Idriss of the Free Syrian Army told the BBC that Hezbollah fighters were "invading" Syria and Lebanon was doing nothing to stop them.
Gen Idriss denied rebels were losing the war, despite recent setbacks.
Early on Wednesday Syrian state TV claimed that government forces had gained full control of Qusair.
There was no way of immediately verifying the claim, which was also reported by Hezbollah's Al-Manar TV channel.
Gen Idriss also said the rebels would not accept any role for President Bashar al-Assad in a post-conflict Syria.
"If the price of peace is that Bashar still has the power in Syria, we don't need that kind of peace," he said.
He said he had told commanders, including those near the strategic town of Qusair, to fight Hezbollah militants "just inside Syria".
But he added: "There are now a very large number of Hezbollah fighters in Syria, in Qusair, in Idlib, in Aleppo, in Damascus and I can say everywhere in the country.
"Hezbollah fighters are invading Syrian territory. And when they continue to do that and the Lebanese authorities don't take any action to stop them coming to Syria, I think we are allowed to fight Hezbollah fighters inside [Lebanese] territory."
Pro-government forces including Hezbollah fighters have been battling rebels for control of Qusair in recent days.
The town lies just 10km (six miles) over the Lebanese border and along major supply routes.
"Our heroic armed forces have returned security and stability to all of the town of Qusair," said Syrian state TV early on Wednesday.
Al-Manar reported "widespread collapse" of the rebel forces in the town.
However the BBC's Jim Muir, in Beirut, said the reports showed no pictures from the town nor details of the alleged victory, and that a similar claim was made two weeks ago.
On Tuesday, activists reports spoke of continued bombardment and clashes, but reported only three fatalities on the rebel side, our correspondent adds.
Gen Idriss said he was sure the rebels would win the fight against Mr Assad.
"But without the support from our friends in Western countries and the USA the fight will continue for many, many years and there will be more martyrs, more destruction," he said.
In that scenario, extremists would win more support within rebel ranks, he added.
More than 80,000 people have been been killed in Syria and more than 1.5 million have fled the country since an uprising against Mr Assad began in 2011, according to UN estimates.