The strikes signalled a tougher Israeli response to the hundreds of balloons and kites carrying firebombs.
Asked what he wanted to see from protests on Monday and Tuesday, Hamas official Yahya Sinwar pointed out Israel has never specifically defined its borders.
Hundreds of refugees on Monday tried to break through a border fence into Macedonia from Greece, where more than 7,000 people are stranded, as anger mounted over barriers to entry imposed on migrants.