Gov. Mills E. Godwin refused today to comment on a statement by U.S. Secretary of Transportation Brock Adams that Godwin "had indicated to me his full completing the Metro rail system."

Asked if Godwin has promised Adams his full support of Metro, John H. Wessells, the governor's press secretary, conferred with Godwin and then is set forth in a letter to Adams's predecessor, William T. Coleman.

That letter, dated Jan. 13, emphasizes Godwin's inability to make any future commitment for the state and promises no support for Metro beyond a recent agreement to use about $75 million in aid in order to win U.S. approval of construction of Interstate Rte. 66 from the Capital Beltway through Arlington to Washington.

Full support of Metro rail would be a reversal of Godwin's previous policy on the rail system. He never has proposed money for Metro construction and last year voted a $10 million appropriation for it by the General Assembly.

He often has called the 100-mile system "unfeasible" because of its high costs, and once referred to it in a press conference as a "boondoggle."

Adams characterized his understanding of Godwin's commitment to Metro on Tuesday when he announced final approval of the 1-66 project. Wessells and Adams aide David Jewell said that the two officials talked about 1-66 and Metro by telephone last week.

Jewell said Adams understood God win to promise that he "would do everything in his power to complete the entire Metro system in Northern Virginia," Wessells, said Godwin would not comment on his conversation with Adams except to say that he is "grateful that he approves of the 1-66 project and hopes constructiong can soon begin."

When former Secretary Coleman gave his approval to 1-66 last month, he said the state government has a "moral obligation" to work for the completion of the Metro system. He acknowledge that the state legally was bound only to provide the $75 million in aid stipulated in the final 1-66 agreement.

In an interview last month, God-win would not comment on Coleman's assertion that the state has a "moral obligation" to contribute to the completion of the system. He also pointed out that he and Coleman were in no position to make commitments for future governments federal or state.

Godwin's term ends next January. His last major responsibility as governor will be to draft a budget for the two years ending in mid 1980.