Supporters of the assassinated president of North Yemen were reported to be in full control of the Red Sea country yesterday but the motives and identity of his killers remained a mystery.

President Ibrahim Hamadi and his brother, Lt. Col. Abdallah Muhammad Hamadi, were assassinated Tuesday, according to government radio broadcasts, but the government has given no details about how they died.

Diplomatic sources here and in Middle East capitals said it would be difficult to immediately assess the impact, if any, that the assassination might have outside the small Arab country, strategically situated between Saudi Arabia and the explosive Horn of Africa.

Three possible motives were suggested by diplomatic sources for an attack on Hamadi: his difficult relations with powerful tribal sheikhs; his efforts to unify his country and Marxist-ruled South Yemen and his alliance with Saudi Arabia in the rivalry between conservative and radical states for influence within the Arab world.

Improved relations between the two Yemens has been a key part of Saudi Arabia's effort to reduce the potential for hostilities in the Arabian Peninsula and to lessen Soviet and radical Arab influence in the Horn of Africa and its surrounding territory.

Saudi Arabia yesterday condemned the assassination as a "treacherous criminal act" and said it would be prepared to aid North Yemen against "evil scheming by malicious people."

South Yemen called Hamadi's slaying "part of the imperialist plot designed to crush the struggle of the Yemeni people."

North Yemen had once relied heavily on Soviet economic and military assistance but it expelled its Soviet military advisers in June 1976. Since then, Saudi Arabia has provided major economic aid and Jordan has sent military advisers.

Saudi Arabia, in recent months, has also stepped up its assistance to South Yemen despite that country's continued friendship with the Soviet Union.

North Yemen's government radio said yesterday that the new rulers would continue Hamadi's foreign policies - which were generally friendly toward the United States - and it called on North Yemen's population of about 7 million to rally under the new leadership and safeguard internal security."

Lt. Col. Ahmed Hussein Ghashimi, the armed forces chief-of-staff who was elevated to replace Hamadi, was described by diplomatic sources as one of the slain president's closest associates.

One U.S. official said it appeared that "everyone has simply moved up a notch" and little change was considered likely in the ideological makeup of the government.

North Yemen was quiet yesterday, according to reports from Sanaa, and no special security buildup appeared to be in effect.

There was no separate confirmation of reports by the Iraqi News Agency that angry crowd had gathered in Sanaa, that the new government had moved troops to key locations there and that another high official had been killed.

Hamadi recently had been trying to work out an arrangement with the powerful tribal sheikhs of his country by which they would disarm their vast private armies in return for greater political roles.

This policy, according to reports earlier this month, produced a split in Hamadi's government with Information Minister Ahmad Damash rejecting it outright.

Another potential source of friction within the ruling circles, observers said, was Foreign Minister Abdallah Asnaj's announcement last week that the country's diplomatic corps would be reshuffled to make it more responsive to reforms ordered by Hamadi.

In recent years, more than half dozen high North Yemeni figures have been assassinated. The most recent was Qadi Abdullah Ali Hajri, a former prime minister, who was shot and killed on a London street in April.

Hamadi himself had come to power in an apparently bloodless coup in June 1974 that put a strongly pro-Saudi government in power.