JERUSALEM — The militant group Hamas used last summer’s war with Israel in the Gaza Strip to carry out extrajudicial killings of at least 23 Palestinians accused of collaborating with Israel and to torture dozens of others, including political rivals, Amnesty International charged in a report issued early Wednesday.

In a reminder of the region’s churning tensions, the Israeli military launched predawn airstrikes on Gaza on Wednesday in response to a rocket fired from the coastal territory the night before.

The rocket landed near Gan Yavne, an Israeli town outside the port city of Ashdod, causing no injuries but puncturing the fragile calm that has mostly prevailed since the 50-day war ended last August.

Israel’s defense minister, Moshe Yaalon, said in a statement that the rocket had been fired by Islamic Jihad, not Hamas, the Islamic organization that controls the crowded coastal territory and has generally tried to enforce an informal cease-fire with Israel. But Mr. Yaalon said that Israel viewed Hamas as responsible. “It is in Hamas’s interest to act to rein in any attempt to fire at Israel,” he said. “Otherwise, we will be forced to act with greater force.”