A separate blast hit a police checkpoint in the Nile Delta in the north of the country. There were no immediate details on that attack.
At about the same time and on the Gaza side of the border, three Palestinian security officers were injured in an exchange of fire with Palestinian militants who tried to ram an explosives-laden car into the main Israel-Gaza crossing, Palestinian security officials said.
The officers opened fire on the car as it approached the Palestinian side of the Karni crossing, the officials said. Unidentified militants in the car returned fire, injuring the three officers. It was not immediately clear what happened to the militants but the car did not explode, witnesses said.
Israel has warned that, since it pulled out of Gaza last summer, Rafa has become a smuggling zone for terrorists and weapons, reports CBS News correspondent Robert Berger.
The attackers hit just two days after a triple bombing that killed 24 at Egypt's Sinai resort city of Dahab on the Gulf of Aqaba.
Wednesday's attack on the multinational base happened just south of the Rafa border crossing to the Gaza Strip and wounded one New Zealander and one Norwegian attached to the multinational force, officials said.
The peacekeeping force was set up as part of the 1979 peace treaty between Israel and Egypt that led to Israel's withdrawal from the Sinai. It is partially paid for by the United States and has U.S. advisers and soldiers attached to it — in addition to soldiers from several other nations, including Canada.
The Sinai — Egypt's desert peninsula that abuts Israel and separates the Mediterranean from the Red Sea — has been wracked by a series of Islamic extremist bombings in the last year and a half.
The multinational force also has a base in southern Sinai.
Egyptian authorities, already struggling with elusive terror cells in the rugged Sinai Peninsula, moved quickly Tuesday — arresting 30 men in the triple bombings that ripped apart a resort town on a tranquil holiday evening.
Radical Muslim groups moved just as rapidly to distance themselves from the Dahab attacks. The leader of Egypt's banned Muslim brotherhood condemned them as "aggression on human souls created by God."
The militant Palestinian Hamas organization called them a "criminal attack which is against all human values."
The targets Monday weren't just Westerners, reports CBS News correspondent David Hawkins, but Egyptians and Egypt's economy.
Egyptian authorities — despite massive sweeps by thousands of troops and hundreds of arrests after each previous Sinai attack — appeared increasingly frustrated by the ease with which terrorists continue to hit the country's vital tourism industry. It brought in $6.4 billion in 2005 and is the top source of foreign exchange.
"This incident is addressed to the whole of Egypt, there is no reason for it other than an attempt to destroy the economy of Egypt by attacking tourism," said Prime Minister Ahmed Nazif as he visited blast victims in a Sharm el-Sheik hospital.
The usually crowded resort of Dahab was all but empty of tourists Wednesday, reports Berger (audio)
President Hosni Mubarak, who oversees an already-stagnant economy with unemployment rising in lockstep with the population explosion, called the attack a "sinful terrorist action."
The attacks came just one day after al Qaeda leader Osama bin Laden had urged Muslims to support al Qaeda in what he called a war against Islam.
Egyptian officials have said local people were behind the previous bombings in the Sinai, but outside security experts say Sinai's extremists seem either al Qaeda linked or at least aligned with its views.
Security officials said the remains of three men recovered from the scene of the blasts were so badly torn apart that they could have been suicide attackers.
Arabs throughout the Middle East voiced outrage, signaling a growing backlash as fellow Muslims increasingly bear the brunt of terrorist attacks. Of the 24 dead in Dahab, 21 were Egyptians.
"I don't think these people care" if Muslims or Arabs are killed. "They'll carry on at any price," said Lara Darwazah, a 31-year-old music teacher in Dubai, United Arab Emirates.
All three Sinai bombings were timed to Egyptian national holidays when resorts were especially crowded with local tourists as well as foreigners who flock to the seaside towns, the world-renowned beaches and extraordinary reefs.
Taba and Ras Shitan in the northern Sinai near the Israeli border were hit and 34 killed in October 2004, a day before the holiday marking the start of the 1973 Arab-Israeli war.
Last July 23 — Egypt's national day — suicide bombers killed 64 people, mainly tourists, in Sharm el-Sheik on the southern tip of the Sinai.
Monday's Dahab bombings occurred on the eve of Sinai Liberation Day, when Egypt regained full control of the peninsula from Israel in 1986. The tourist population was swollen further by the coincidence of the long Coptic Christian Easter weekend and an ancient Egyptian holiday to mark the start of spring.
Egypt's Sinai resorts are a tempting and virtually made-to-order target for Islamic militants who were jailed by Mubarak or fled to safer territory and became even more radical- witness Egyptian physician Ayman al-Zawheri's migration to Afghanistan and the No. 2 place in al Qaeda.
The isolated and desolate peninsula also has become a favored Israeli holiday destination, making bombings there both a symbolic attack on Israelis and an assault to undermine Mubarak's authority and rattle his tenuous economy.
Interior Minister Habib el-Adly said it was not immediately clear if the attack could have been carried out by a group as organized as those who detonated the earlier bombs. He said the explosives were different than those used in Sharm el-Sheik or Taba.
The World Economic Forum said it would go ahead with plans to hold a meeting of Middle Eastern government and business leaders in Sharm-el-Sheik on May 20-22.
"For the sake of a more peaceful future for humankind we have to show our solidarity by holding this meeting," said Klaus Schwab, the Geneva-based convener of the forum, in a letter to Mubarak.