"We never took an initiative to fire," Peres said. "And we don't take any advantage of the civil war in Syria. We don't consider that we should or can intervene."
He added, however, that "if they want to have an additional war ... well, that's their choice."
The Israeli Defense Forces reported that there was no damage and no injuries, but the latest fire portends how what's happening in Syria could seriously rattle the entire region.
The Golan is regarded internationally as occupied territory despite Israeli governmental control. It is home to 41,000 residents, including Jews, Druze and Alawites. Israel seized the territory from Syria during the 1967 Israel-Arab war, and it was eventually annexed.
In addition to returning fire, Israel filed a complaint with the United Nations forces operating in the area.
Fire coming from Syria into Israel "will not be tolerated and shall be responded to with severity," the complaint said, according to Israeli military sources.
Israeli Lt. Col. Avital Leibovich said she doesn't think the fire from Syria into Israel was intentional.
"We interpret it as ... leaks into Israel territory," she said. "It's totally internal conflict in Syria. We believe that Israel is not the target here. We are looking at either stray bullets or stray mortars."
Peres said he hopes Syria won't make the same mistake again. Syria "must understand their own limitations," he said. "But if it ever happens, we shall defend ourselves -- that's what I can say. I don't want to exaggerate and to make great declarations and bellicose interests."
Peres continued, "No, we are not interested. We understand that Syria has enough problems of their own. And it doesn't give us again any pleasure. But if they endanger our lives, we shall defend ourselves. That's what I can say in a certain manner. And I don't want to fire declarations because I don't like fire -- unnecessarily anyway."
U.N. Secretary-General Ban Ki-moon reacted with a statement Sunday saying he "is deeply concerned by the potential for escalation."
"He calls for the utmost restraint and urges Syria and Israel to uphold the Disengagement Agreement, respect their mutual obligations, and halt firing of any kind across the cease-fire line," the U.N. statement said.
Israel's ambassador to the United States, Michael Oren, told CNN Sunday that "a greater possibility" from the exchange of fire "is the inundation of refugees -- Christian, Druze, Alawites."
"We'd give them refuge," Oren said. "These are populations with which we have good relations. It's not unprecedented. We've been prepared for it for a long time, but it hasn't happened."
Peres, asked whether Israel would accept refugees from Syria, said: "There are 24 Arab countries. There is one Jewish country. There are places. They speak Arabic. They are Muslims. Why should they come to Israel?"
He noted that there are Muslims in Israel, "and we respect the Muslims here. They are our citizens."
But, he said, "to add more doesn't make sense. There is a huge Arab world. Israel is ... of the space of the Middle East. ... They want to be Muslims. They want to be nations. Why create an artificial problem? What for?"
The solution, he said, is "to stop the war and not create more refugees."
Sunday's incident in the Golan Heights area is the fourth U.N. complaint Israel has filed. So far no one has been injured.
Syrian tanks entered the Golan Heights demilitarized zone last week and fired into Syria; bullets fired at the tanks in response struck an Israeli military vehicle in part of the Golan Heights that Israel claims as its own. Mortars also fell in part of the Golan that Israel considers its territory.