The strikes followed fierce exchanges over the weekend in which Israeli ground forces killed two Palestinian teenagers in the enclave in cross-border fire.
Two of the men were severely wounded but their lives were not in danger, the army said.
"The U.S. ignored throughout the history of the [Arab-Israeli] conflict the right of the Palestinian people to live in security and peace on their land", Hamas said.
The rocket, fired late Sunday, reportedly landed in an open area in the Sha'ar Hanegev region bordering the Strip.
No terror organization took responsibility for the attack, but the increase in rocket fire from the Strip over recent months has mostly been the work of an Islamic State (ISIS) affiliate operating out of Gaza.
Saturday's military escalation between Israel and Gaza militants coincided with the visit of a senior Hamas delegation headed by its political leader Ismail Haniyeh in Cairo, Egypt since last week.
"In my evaluation, the thing won't exceed the routine and regular Israeli army retaliation against militants' attacks", he said.
The GRM is a temporary agreement among the Palestinian National Authority, Israel and the United Nations that went into effect after Israel's 2014 major offensive on Gaza.
"Hamas is responsible for anything that happens in the Strip and whatever comes out of it, both over and underground", the IDF said in a statement.
COGAT, Israel's military liaison to the Palestinians, said that from now on rioting at the border fence will be met with a tougher response, after four IDF soldiers were injured by an improvised explosive device that was apparently planted there during one of the riots. Israel responded to the attacks by eliminating 18 terror targets in Gaza, including Hamas weapons factories. Two Palestinians were killed, according to the Hamas-run Gazan health ministry.
Tensions between Palestinians and Israelis have been running high since December, when US President Donald Trump recognised Jerusalem as the capital of Israel.
Liberman's comments on Monday about the northern border were in reference to a recent confrontation between Israel, Iran, and the Assad regime on the northern border over a week ago.