The Carter administration has taken a new legal position that would permit federal funds to be cut off in desegregation cases where communities have been required to merge schools.

Under a new interpretation, the Department of Health, Education and Welfare could withhold money in cases where schools are paired or clustered to achieve desegregation.

The new position presents a test of the so called Byrd amendment, which prevents HEW from withholding funds to force school districts to use busing to desegregate schools. Some busing is often required in cases involving merged schools - those in which black and white schools are paired or clustered to desegregate classrooms in both.

HEW Secretary Joseph A. Califano Jr. took the position that the Byrd amendment did not preclude cutting off funds in cases involving pairing or clustering of schools.

He was supported in a memorandum, released yesterday, from Attorney General Griffin B. Bell, which agreed that in any litigation arising over paired schools the Justice Department would support Califano's position.

The issue arose in HEW's preparation for a case involving Kansas City, Mo., schools. Califano had been asked by Sen. Thomas F. Eagleton (D-Mo.) that position the department would take.

The amendment was sponsored by Senate Majority Leader Robert C. Byrd (D-W. Va.) and first applied to HEW's appropriation bill for fiscal year 1976.

Civil rights lawyers interpreted the new position as a stronger assertion of the obligation to desegregate and a shift from the position taken by the Ford administration. They said HEW's Office of Civil Rights formerly had contended, in a California case, that it was precluded by the Byrd amendment from cutting off funds where a school district balked at paired and clustered schools.

In a paired-school case, a predominantly black school will be merged with a predominantly white one by assigning all students in some grades - one through four, for example - to one school and all students in the remaining grades to the other.

Clustering involves the same assignment process applied to three or more schools in a community.