Two street explosions within minutes of each other in Riyadh last night killed one person and injured three, according to reports from the Saudi Arabian capital. An anonymous caller told a foreign news agency here today that the explosions were carried out by the Islamic Jihad group as the opening of a campaign to bring down the Saudi monarchy.

Official Saudi accounts of the explosions gave no indication of who might have been responsible for the bombings, the first known acts of terrorism in the Saudi capital in recent years.

Iran's official news agency IRNA accused Iraq today of causing the explosions, to sabotage Saudi-Iranian relations and disrupt the visit to Tehran of the Saudi foreign minister, Prince Saud. Saud went to Tehran yesterday on the first official visit by a member of the Saudi royal family since Iran's Islamic revolutionary government took power in 1979.

The official Saudi Press Agency said last night that one person was killed and three injured when dynamite in two trash cans exploded. A Saudi Interior Ministry spokesman said later that the dynamite was of the type usually used on construction sites and that an official investigation had begun.

Residents of the area, according to Reuter, said the explosions were about a mile apart, on a busy commercial street in the Sulaymaniye area of northern Riyadh. One of the blasts reportedly was across the street from a complex housing American advisers to the Saudi Arabian National Guard. The victims were not identified.

The caller purporting to speak for Islamic Jihad said: "Our cells acting in Saudi Arabia have started carrying out the operations assigned to them in order to shake the reactionary Saud dynasty. Actually we planted several charges, some of which were detonated by wireless and some were hurled at the curbs."

The caller said that the explosions were "but a minor specimen of a series of blows that we are planning in various Saudi towns and official departments." He charged that the house of Saud had "seized by force and trickery the holiest land of Islam" and added that "we shall therefore plot earnestly with other Moslem believers to regain power and oust the despots."

Shiite Moslems are a minority in Saudi Arabia, and many Shiites there and elsewhere strongly resent the unification of the peninsula in 1926 from a group of warring tribes into a kingdom ruled by the house of Saud, which considers itself the caretaker of Islam's holiest shrines and whose members are Wahhabis, a 19th century puritanical movement of Sunni Moslems.

In November 1979, when a group of Wahhabi extremists seized the Grand Mosque in Mecca, disturbances also broke out in the Eastern Province, where most of the country's Shiite minority lives.

Scoffing at the Saudi foreign minister's sudden visit to Tehran, the Islamic Jihad caller said today, "Let no one think that attempts at a rapprochement with the Islamic republic Iran will deter us or make us hesitate in carrying out" the threats.

Islamic Jihad, which claimed responsibility for the American Embassy bombings here and the suicide attacks on the U.S. Marine and French military headquarters in 1983, as well as recent bombings in Paris and Madrid, has said it is holding most of the American and other western hostages kidnaped in the Moslem-controlled sector of Beirut in the past year.

It has sought the release of 17 persons held in Kuwaiti prisons in connection with bombings at embassies and government offices there on Dec. 12, 1983, and it recently offered to free the U.S. and French hostages in return.

Arab sources have been quoted as saying that the announcement by Islamic Jihad of its offer jeopardized delicate negotiations on the issue through Arab mediators believed to be close to Iran. Tehran has dissociated itself from the movement although it is believed to have close links to it.

Iranian President Ali Khamenei scoffed at U.S. warnings of reprisals against Iran if Americans held by Islamic Jihad are hurt, United Press International reported. The official Islamic Republic News Agency quoted Khamenei as telling government officials in Tehran on Sunday: "These threats by American politicians are worthless."

In Beirut, meanwhile, heavy shelling overnight across the line separating Moslem west Beirut and Christian east Beirut left three persons dead and at least 20 wounded. The Baabda palace of President Amin Gemayel, a Christian, was hit by machine-gun fire today but no casualties were reported.