The camp in the town of Kilis is occupied by thousands of people who fled to escape the continuing violence in Syria.
The Turkish Foreign Ministry said in a statement Syrians who seek shelter in Turkey would receive the country's "full protection" and said "the necessary measures will be implemented if such incidents [cross-border shootings] are repeated," the Hurriyet Daily News reported.
The statement called the gunfire a "grave" development.
Meanwhile, Voice of America reported a Lebanese cameraman was shot and killed on the Lebanese side of the border by gunfire coming from Syria.
On Tuesday, United Nations envoy Kofi Annan will visit camps housing Syrian refugees.
The Syrian Foreign Ministry, referring to the Annan-U.N.-backed plan for a Tuesday cease-fire, said it has not received assurances that "armed terrorists groups" in the country will respond to the deadline, the Daily News said.
Today's Zaman noted Turkey's President Abdullah Gul and Defense Minister Ismet Yılmaz have not ruled out a military response.
Security agreements over the past decade allow Turkey to intervene in Syria if the security situation in that country threatens Turkey's national security. Today's Zaman said Turkey could invoke the NATO charter, which says an attack on any member would be considered an attack on all members.
The Assad regime allows the Kurdistan Workers' Party and its affiliates to carry out attacks on Turkish soil and about 1,500-2,000 PKK militants are in Syria near the Turkey border. Thus, Turkey could intervene based on the NATO charter as a "last resort," Today's Zaman said.
Annan misread Syria's pledge to remove troops Tuesday, a regime spokesman declared, saying rebels and their backers must halt first.
"To say that Syria will pull back its forces from towns on April 10 is inaccurate," the Syrian Foreign Ministry said in a statement Sunday.
"Annan has not offered written guarantees to the Syrian government that the armed groups agreed to stop violence, nor has he offered guarantees that Qatar, Saudi Arabia and Turkey will commit to stop funding and arming terrorist groups," the official Syrian Arab News Agency reported, citing Foreign Ministry spokesman Jihad Makdessi.
Makdessi alleged the United Nations failed to hold the opposition to account in the peace deal, it said.
"Syria won't repeat what happened during the Arab monitors' mission when it committed to pulling out troops from cities, which the armed groups used for reorganizing and arming their members and took over whole neighborhoods, which prompted the Syrian armed forces to interfere in response to appeals by citizens," SANA said, referring to an ill-fated monitoring mission sponsored by the Arab League in December and January.
The Free Syrian Army, the opposition's main fighting wing, said the Assad regime's actions show why rebel fighters would not lay down their arms first.
"We can't drop our guns until the regime withdraws from the cities," Free Syrian Army Lt. Abdullah Odah was quoted by CNN as saying in Istanbul, Turkey.
"We didn't start the mass murder. The regime started it. It has to stop killing and then automatically we will stop," he said.
The cease-fire plan called for Syrian forces to withdraw from cities and towns by 6 a.m. local time Tuesday and for the government and opposition fighters to lay down their arms by 6 a.m. Thursday.
Some Syrian activists blamed the former U.N. secretary-general for being gullible enough to believe President Bashar Assad had any intention of compromising.
Annan said in a statement, "As we get close to the Tuesday 10 April deadline, I remind the Syrian government of the need for full implementation of its commitments and stress that the present escalation of violence is unacceptable."
He called the sharply escalating violence a "violation of assurances given to me."
At least 40 people were killed Sunday, a day after 127 people died in crushing assaults across the country, the opposition Local Coordination Committees said.
Video posted on YouTube Sunday purported to show MiG-29 jet fighters flying over Syria's largest city, Aleppo, as well as military helicopters firing rockets and alleged members of the notorious civilian-clothed shabiha paramilitary gangs in the southwestern city of Daraa, near Jordan, cursing and manhandling the bodies of dead rebels.
None of the information and video about the fighting could be independently confirmed because the Assad regime has severely restricted access to international media.