An Israeli airstrike in northern Gaza early on Thursday killed a Palestinian, while a second man died from wounds sustained in last week's mass protest along the Gaza-Israel border, officials said.
The fatalities bring to 21 the number of people killed in confrontations in the volatile area over the past week.
A new round of protests along the border is expected on Friday, raising the prospect of further bloodshed.
The protest march last week, largely organized by Gaza's Hamas rulers, had been billed as the first of several weeks of intermittent protests against a stifling decade-old Israeli blockade.
Hamas leaders have portrayed the final protest, set for May 15, as the "Great March of Return" of Palestinian refugees and their descendants, implying they would try to enter Israeli territory. But they have stopped short of specifically threatening a mass breach of the border fence.
The Israeli military has said it will not allow anyone to breach the border fence and has beefed up forces in the area, with snipers and other special units. The military was on high alert ahead of Friday.
Nickolay Mladenov, the U.N.'s Mideast envoy, urged both sides to show caution on Friday.
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"Israeli forces should exercise maximum restraint and Palestinians should avoid friction at the Gaza fence," he said.
"Demonstrations and protests must be allowed to proceed in a peaceful manner," he added. "Civilians, particularly children, must not be intentionally put in danger or targeted in any way."
In the latest violence, the military said an aircraft had targeted an "armed terrorist adjacent to the security fence" in northern Gaza early in the morning. The Gaza Health Ministry confirmed the man's death but did not immediately release his identity.
It also confirmed the death of a man who was wounded in last Friday's protests. Hundreds more were wounded by live fire last week, according to Palestinian health officials. Of the 21 dead so far, 15 were killed during border protests, and videos and witness accounts indicate that most were not armed or carrying out attacks at the moment they were killed.
Israel has defended its actions by saying the marches are planned by the militant Islamic Hamas group, which is sworn to Israel's destruction. It says the border fence was attacked with burning tires, stones and firebombs, and in one case, by a pair of gunmen. It says its snipers carefully targeted only the main "instigators," and accuses Hamas of using the crowds as cover to stage attacks.
"By defending the border fence, the IDF is protecting civilian homes," the military said on Twitter, referring to the Israel Defense Forces.
Defense Minister Avigdor Lieberman warned in a radio interview on Thursday that Israel would respond harshly to any attempt to violate its security. Earlier this week, Lieberman said Gazans who approach the fence would be risking their lives.
Rights groups have condemned orders to shoot unarmed protesters as unlawful, saying lethal force can only be used if soldiers face an apparent imminent threat to their lives. The Israeli group B'Tselem, in a rare appeal, urged Israeli soldiers to refuse such orders.
The United Nations and the European Union have called for independent investigations into the shootings.
Meanwhile, Egyptian intelligence chief Abbas Kamel held separate meetings this week with Israeli officials and with Palestinian President Mahmoud Abbas, the West Bank-based rival of Hamas, in hopes of preventing an escalation on the Gaza border.
In recent months, Egypt had tried to broker a deal that would have enabled Abbas to take back control in the Gaza Strip, more than a decade after Hamas seized the territory from forces loyal to him.
Hamas, in turn, had hoped that Israel and Egypt would end their blockade Gaza if the group handed the reins of government to Abbas. However, talks broke down last month, in part because Hamas refused to disarm.
Hamas and Israel have fought three wars in the Gaza Strip since 2009.
Abbas told the Egyptian intelligence this week that he would not waste any more time negotiating a deal with Hamas and that he would only assume responsibility for Gaza if Hamas hands over all powers, including control over the security apparatus, according to two Palestinian officials.
All the officials spoke on condition of anonymity because they were not authorized to discuss details of the meeting with reporters.
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Associated Press writer Mohammed Daraghmeh in Ramallah, West Bank, contributed to this report.
