A rocket fired from Syria hit the Israeli-occupied sector of the Golan Heights on Sunday, falling on open ground and causing no casualties, an army spokeswoman told AFP.
"The assumption is that it was not a stray," she said.
And early on Monday the army said that "several rockets were fired from Lebanon at the western Galilee, one hitting an open area. No injuries reported thus far".
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The army said Israel responded with artillery fire at Syrian military posts and that "hits were identified" and that it also shelled the source of the fire from Lebanon, lodging a complaint with UN peacekeepers there.
An Israeli Arab teenager was killed on the Golan border last month by what may have been a rocket, mortar fire or an explosive device, prompting Israel to carry out retaliatory air raids on Syrian army positions.
Sunday's incident was the first of its kind from Syrian territory since Israel on Tuesday launched a fierce air campaign on Gaza with the stated aim of stemming a rising tide of rocket fire by Palestinian militants.
But rockets fired from Lebanon struck northern Israel on Friday and Saturday, without causing casualties.
Military officials said they believed the attacks were carried out by a small Palestinian group in an act of solidarity with Gazan militants.