United States President Donald Trump's decision to recognise Jerusalem as Israel's capital has prompted global criticism and sparked protests across the world.
The Iron Dome aerial defense system intercepted two rockets launched from the Gaza Strip, the Israeli Defense Forces (IDF) posted on Twitter.
There were no immediate reports of casualties in the exchange of fire, the first in more than 10 days.
Israel police confirmed that a third rocket struck Nahal Oz area, which is located in the northwestern part of the Negev desert close to the border with the Gaza Strip, causing damage to a building but no injuries.
It said plumes of smoke were visible from one of the targeted areas east of the Gaza City neighbourhood of al-Tuffah. A spokesman for Hamas said it didn't fire the rockets but had erected the sign.
Both Hamas and fellow militant group Islamic Jihad had labelled Friday a "day of rage", as in previous weeks.
Rocket warning sirens were heard shortly before midday in the Shaar Hanegev and Sedot Hanegev regions, sending frightened residents running to shelters.
The Israeli army said there were "very small clashes" in a number of sites.
The strikes came "in response to the rockets fired towards Israel" earlier on Friday, according to the statement.