President Carter met for an hour yesterday with six Democratic governors but made no commitments that he will shape his proposed national water policy according to the governors' recommendations.

Gov. Scott Matheson of Utah, chairman of the National Governors' Association subcommittee on water management, said after the meeting that the major point of disagreement between the governors and the administration is the question of sharing the cost of water projects.

Historically, the federal government has paid the full cost of water projects such as construction of dams. But one of the major options being considered by Carter for a proposed national water policy would require the states to pay 10 percent of a project's cost as construction began.

Matheson said the governors favor "the concept of cost sharing," but oppose legislation that would require the states to pay a certain amount of each water project. Instead, he said, the governors favor a voluntary system under which each state depending on its financial situation, would determine how much of each water project it could pay.

Officials of the National Governor's Association said such a voluntary system presupposed that projects for which a state is willing to share the cost would receive priority in federal appropriations. An across-the-board requirement that each state pay a fixed amount, the officials said, could impose severe hardships on states such as Colorado, which does not have authority to issue bonds.

Matheson said the governors also want those water projects already approved and partially funded by the federal government exempted from any cost-sharing provisions. He said, however, there is not agreement among all the governors on this issue, with some governors favoring even more extensive exemptions.

Matheson said the president listened to the governors' proposals but made not commitments.

Carter has promised to develop a national water policy since early in the administration when he sought, unsuccessfully in most cases, to block construction of several water projects. The policy, already behind schedule in its development, is expected to be unveiled in a few weeks.