Japanese radicals, overcoming an unprecedented blanket of police security, fired five handmade rockets toward Tokyo's Akasaka Palace today as opening ceremonies for the seven-nation economic summit were taking place there.

Police said all the rockets fell far from the building and caused no injuries or significant damage.

The attack, a major embarrassment for the Tokyo police, took place as Japanese Prime Minister Yasuhiro Nakasone was officially welcoming French President Francois Mitterrand at the palace amid the pomp of trumpets, red carpets and a military honor guard.

The rocket attack came on a day when mildly radioactive rain, believed to be from the Soviet nuclear reactor accident at Chernobyl, began to fall on several areas of Japan.

Although the rockets fell harmlessly and the radioactivity was not judged to be health-threatening, the two events provided a grim backdrop to an economic summit meeting. The seven national leaders spent their first official dinner meeting discussing international terrorism and the Soviet nuclear accident rather than economics.

The leaders of the United States, Canada, West Germany, France, Britain, Italy and Japan agreed at that dinner to have working groups try to draft statements for endorsement by the summit on terrorism and the Soviet nuclear accident.

There was no indication tonight that the attack would cause any change in proceedings at the summit, except for even heavier security. President Reagan, asked later in the day by reporters if he was concerned about the attack, quipped, "No, they missed." Reagan had not yet arrived at the palace when the attack was launched.

British Prime Minister Margaret Thatcher said she had been unaware of the attack, but "I think it does underline the importance of discussing terrorism" at the summit.

The rockets, which apparently carried small explosive charges, flew unguided for about two miles. The nearest hit was about 600 yards away, but a direct hit on the palace conceivably could have caused serious injury or even death at the ceremony. Officials were unable to say whether Nakasone and Mitterrand were outside or inside at the time of the attack.

"I am filled with anger," Chief Cabinet Secretary Masaharu Gotoda told reporters tonight, vowing to tighten security.

The metal rockets were fired from tubes sticking out of the window of an apartment in the city's Shinjuku district, about 1.6 miles from the palace. The bases of the tubes were set in concrete, and the rockets were fired by automatic timer. Authorities arriving at the scene found the apartment's door locked and no one to arrest.

Two of the rockets landed near the Canadian Embassy, located just outside the large grounds of the palace.

No one had asserted responsibility for the attack as of tonight. But police said the rockets resembled primitive ones used in past attacks by a leftist group known as the Middle Core Faction.

Earlier in the day, 1,100 of the group's supporters, many of them wearing masks and helmets, staged a rally and march against the summit. They have vowed to "destroy" it, saying it is a conference for world war. About 1,400 other radicals demonstrated against it in two other rallies.

The attack followed several similar rocket firings against Japanese and American targets in Tokyo and a U.S. Air Force base. The attacks usually seem intended more to taunt the police and cause confusion and panic than physical damage. Police here say that the group appears to have no connection to international terrorist organizations.

With 15,000 officers, police had created a security zone in a radius of about 1.2 miles around the palace, inspecting about 50,000 houses and buildings. Gotoda said the size of the security area was based on authorities' belief that the radicals' rockets could only fly about that distance. However, Tokyo newspapers have reported recently that police had intelligence that the radicals were developing a longer-range rocket.

Gotoda said tonight that police would expand the zone.

Meanwhile, the Japanese news media gave prominent attention to a government announcement that unusually high levels of radioactive Iodine 131 had been detected at several points around the country, including Tokyo. In an emergency session this morning, a special atomic energy agency advised Japanese to avoid drinking rain water, or at least to purify it with charcoal filters, and to wash vegetables thoroughly.

Officials stressed that the health hazard was not significant. But because of the atomic bombings of World War II, this society remains highly sensitive to anything involving nuclear energy. Government offices got large numbers of calls from worried citizens.

A statement condemning the Soviet Union's handling of the accident, which sent radioactive particles over much of Europe, is expected to be issued at the summit meeting. News of the radiation could harden Japan's stance.

It was unclear what effect the news would have on Japan's own nuclear energy program, which has an excellent safety record. The country has 32 nuclear power plants in operation, providing about 26 percent of all electricity generated here. Ten more are under construction, and more are planned. With no significant oil resources of its own, Japan has placed a high priority on nuclear energy to reduce dependence on oil imports.

Activist groups that oppose nuclear weapons and energy quickly cited today's reports as proof of their positions.