JERUSALEM — The tenuous cease-fire in the 50-day war between Israel and Gaza militants was deeply strained Wednesday by a clash that Israel’s military said had been started by a Palestinian sniper attack on a routine border patrol.

The clash left one Palestinian militant dead and an Israeli soldier wounded. It appeared to be the most serious direct confrontation between Israel and Hamas, the Islamic group that dominates Gaza, since fighting was halted in late August.

After the patrol on the Israeli side of the border came under fire, the Israeli military said, Israel responded with air and ground forces against Hamas positions in the immediate vicinity of the attack.

A spokesman for the Health Ministry of Gaza identified the Palestinian who was killed as Tayseer al-Samari, 33. The military wing of Hamas immediately claimed Mr. Samari as one of its own, and it said he was the head of the group’s reconnaissance unit in southern Gaza.