Israeli troops shot and killed three Palestinians near the Israel-Gaza border fence at the Kissufin crossing, Tuesday.
The Israeli army said soldiers opened fire after spotting suspicious people near the fence.
Israeli soldiers arrested at least five suspected Palestinian militants after a brief exchange of gunfire near another Gaza border crossing. One of the militants was wounded. The Israeli military said the firefight broke out when soldiers surrounded a house where the militants were holed up.
Palestinian witnesses say a large number of soldiers backed by tanks and helicopter gunships took part in the operations at Karni - the main terminal for transport of goods between Israel and the Gaza Strip.
Witnesses said Israeli tanks and bulldozers also destroyed farmlands near the town of Khan Yunis.
Israeli forces have been carrying out brief incursions into Gaza since launching an offensive in late June to stop cross-border rocket attacks and rescue a captured Israeli soldier.
Some information for this report was provided by AFP, AP and Reuters.