U.N. Mideast envoy Nickolay Mladenov urged Israel and Hamas to step back "from the brink" after both sides exchanged rocket fire Wednesday.
"The situation can rapidly deteriorate, with devastating consequences for all people," Mladenov said.
Militants fired around 70 rockets into Israel from Hamas-controlled Gaza. Israel responded with airstrikes, killing at least one Palestinian and wounding five others, according to the Gaza health ministry.
The violence came even while both sides expressed some optimism that a truce could be worked out to help avoid another war between Israel and Hamas.
"We can say that actions led by the United Nations and Egypt are in advanced stages and we hope it could yield some good from them," the deputy Hamas chief for Gaza, Khalil al-Hayya, told Al Jazeera television.
A senior member of the Israeli parliament said he "very much hopes we are on the brink of a new day on the matter of Gaza."
Palestinians have held weekly protests along the Israeli-Gaza border since March, when Israel began preparations for marking its 70th anniversary as a state.
Israeli soldiers have killed at least 158 demonstrators, many of whom were militants that Israel said were trying to sneak across the border.
Israel accused Hamas of organizing the protests as a cover for terrorism, a charge Hamas denies.