Turkey returned fire after Syrian mortar bombs landed in a field in southern Turkey on Saturday.
It was the fourth day of Turkish retaliation for firing by Syrian forces that killed five Turkish civilians on Wednesday.
The exchanges are the most serious cross-border violence in Syria's conflict, which began as a democracy uprising but has evolved into a civil war with sectarian overtones. They highlight how the crisis could destabilise the region.
Nato member Turkey was once an ally of Syrian President Bashar al-Assad but turned against him after his violent response to an uprising in which, according to the United Nations, more than 30 000 people have died.
Turkey Prime Minister Tayyip Erdogan said on Friday his country did not want war but warned Syria not to make a "fatal mistake" by testing its resolve. Damascus has said its fire hit Turkey accidentally.
Turkish Foreign Minister Ahmet Davutoglu said on Saturday that Parliament's authorisation of possible cross-border military action was designed as a deterrent.
Western powers have backed Turkey over Syria but have shown little appetite for the kind of intervention that helped topple Libya's Muammar Gaddafi. Turkish calls for a safe zone in Syria would require a no-fly zone that Nato states are unwilling to police.
Arab League chief Nabil Elaraby in a newspaper interview called Brahimi's Syria mission "virtually impossible". Asked about the efforts of the Egypt-Saudi-Turkey-Iran quartet to solve the crisis, Elaraby said: "The solution must comprise Iran. The important thing is that matters get moving."
The 18-month-old Syrian revolt increasingly pits a Sunni Muslim opposition against Assad's Alawite minority, an offshoot of the Shi'ite Islam that dominates in Iran, whose government backs Assad's government.
Rebels in the Syrian city of Aleppo said government troops tried to storm the Sakhour district on Saturday but were pushed back after heavy clashes. Activists across Syria said there was fighting in several cities and towns including the central city of Homs and in Damascus countryside.
The British-based Syrian Observatory for Human Rights said at least 60 people, including 36 government soldiers, were killed in clashes across the country on Saturday.
Syrian rebel forces are riven by divisions but Syrian government forces appear to lack the numbers to land a knockout blow and permanently hold rebellious areas.
US President Barack Obama on September 25 accused Iran of helping keep Assad in power but has refused to arm Syria's rebels, partly for fear some of those fighting Assad's rule are Islamist radicals equally hostile to the West.
"Whether or not that conflict begins to extend into the neighbouring countries such as Turkey remains to be seen. But obviously the fact that there are now exchanges fired between these two countries raises additional concerns that this conflict could broaden," Panetta told a news conference in Lima with Peru's defence minister.
Iran on Saturday called for the immediate release of Iranians held captive by Syrian rebels and said it would hold the rebels and their supporters responsible for their lives.
Mortars land in Turkey
It said the fire appeared to have been aimed by Syrian forces at rebels along the border. There were no casualties. Turkish border troops fired back mortars in response.
There were two similar incidents in Hatay on Friday, when Erdogan issued his warning.
"We are not interested in war, but we're not far from war either. This nation has come to where it is today having gone through intercontinental wars," he said.
Turkish artillery bombarded Syrian military targets on Wednesday and Thursday, killing several Syrian soldiers after Syria's initial fatal bombardment. The UN Security Council condemned the original Syrian attack.
Wednesday's Syrian strike on the town of Akcakale was of a different magnitude to previous incidents, a Turkish official told Reuters.
"Wednesday was different. There were five or six rounds into the same place. That's why we responded a couple of times, to warn and deter. To tell the [Syrian] military to leave. We think they've got the message and have pulled back from the area."
Syria has since ordered its warplanes and helicopters not to go within 10km of the Turkish border and artillery units not to fire shells close to the border, according to Turkish broadcaster NTV. Syria has not confirmed this.