The chief of South Africa's 6 million Zulus met with President Reagan at the White House yesterday and strongly supported the president's refusal to impose economic sanctions on the nation because of its policy of apartheid.

In comments during which he expressed disapproval of any use of economic sanctions against South Africa's white-minority government, Chief Gatsha Buthelezi appeared sympathetic to the Reagan administration's controversial "constructive engagement" policy, which emphasizes quiet diplomacy and behind-the-scenes persuasion.

That policy has been a principal target of demonstrators who have been arrested in large numbers at South African facilities here and around the nation.

The demonstrators contend that the policy provides comfort to the regime. Since Thanksgiving eve, 792 persons protesting South Africa's system of apartheid, or white-minority rule, have been arrested at the South African embassy here. Five were arrested yesterday.

In opposing economic sanctions Buthelezi told reporters that a halt to investment in South Africa would mean that "my people would suffer." He added: "It is no use throwing away the baby with the bathwater."

Buthelezi said that "in principle there is nothing wrong with constructive engagement if it is given flesh," apparently referring to the need for more funds for health and education. At present, he said "the ordinary black South African cannot say that he sees anything different in his life because of constructive engagement."

A spokesman for the group that has been coordinating the protests against apartheid expressed disappointment over the actions of the chief minister of the Zulu homeland, whom he described as "on the payroll of the South African government."