In his final speech to the Virginia General Assembly, departing Gov. Mills E. Godwin said today he is proposing a budget for the next two years that will not require any tax increases but will provide only limited state support for the Metro subway system in the Washington suburbs.

Godwin said his $9.1 billion budget for the 1978-80 biennium, an increase of nearly 20 per cent over current spending, would give the state "continued momentum." But he warned that there is little unallocated money in his proposal and that there are "unmet requests" from state agencies excluded from the budget that total $470 million.

In a nearly 50-minute speech that often was a reprise of themes Godwin had developed during his eight years as governor, he also told the 140 legislators to be wary of excessive federal goverment influence and urged them to keep the state on its conservative course.

He said he will not make a decision on the controversial issue of state funding of abortions for indigent women before leaving the choice to the legislature. He also counseled the legislators to find a "workable solution" to the problem of Virginia cities' annexation of adjoining county land, which he called "this major problem of our time, the fate of the core city."

If the Assembly does not deal with the annexation issue, he said "we have before us in the nation's political capital across the Potomac, and its cultural and financial capital across the Hudson, two glaring examples of what continued procrastination will mean." He did not elaborate about his references to Washington and New York City.

The speech made before the opening session of the General Assembly, was a somewhat bittersweet occasion, filled at once with the sadness of Godwin's departure after 30 years in Virginia public life, including two nonconsecutive terms as governor, and the disappointment many legislators - particularly Northern Virginians - felt about what he said.

Godwin, who served one term as a Democrat and this last one as a Republican, leaves office Saturday when Republican John N. Dalton is sworn in Virginia governors cannot succeed themselves.

Godwin projected a 19.5 per cent increase in state revenues during the next biennium beginning July 1, a total of about $730 million. He also said the proposed budget would reflect a surplus of $66.4 million from the current biennium as a result of austerity measures he took during the last four years, such as not filling vacancies in state government jobs.

"The balance, plus a rebounding economy and the reduced pressure on the operating fund from the passage last fall of the $125 million bond issues, enabled me to offer you a budget with continued momentum and without a tax increase," he said. But he warned that the unresolved national issues of energy and tax reform may change the revenue projections.

Godwin recommended that $3 million be added to the current $10 million contribution toward metro subway construction. The $10 million for Metro in the current budget, however, is still tied to gubernatorial approval of a new financing plan by Metro. Godwin suggested that a deadline of July 1, 1979, be set for delivery of the plan before the $10 million is released. "We cannot wait forever," he said.

This aspect of Godwin's speech particularly disturbed Northen Virginians, who say that funding for the Washington metropolitan area subway system is one of their most crucial problems. Some questioned Godwin's claim that $139 million has been spent by Virginia on Metrorail. "This is six times the total in the state funds flowing to all our metropolitan areas combined," Godwin said.

Del. Warren E. Barry (R-Fairfax) said Godwin's remarks had "poisoned the mind" of the Assembly against increased funding for the Metro system.

Sen. Wiley F. Mitchell (R-Alexandria) called Godwin's speech a mixture of "the good, the bad, and the inexplicable. The good he was responsible for, the bad he fought, and the inexplicable is how he got all that aid for Metro."

The contribution to Metro from state taxes and federal funds under state control has come from these sources: $35 million from gasoline taxes, an amount agreed to when the gasoline levy was last increased; about $35 million from a promised transfer of interstate highway funds to Metro, agreed to by the state in order to win approval of construction of Rte. 1-66 through Fairfax and Arlington counties; about $35 million in Metro right-of-way construction costs to be provided by the state as it builds 1-66; $25 million appropriated directly for Metro construction in the last two biennial budgets. The balance has consisted of smaller appropriations in earlier years and appropriations for the administrative costs of the Northern Virginia Transit Commission (NVTC).

"I have consistently said that I felt Metrorail might be a necessary part of unsnarling the traffic jams in and out of the nation's capital," Godwin said, "I have said just as consistently that my objection was to the astrenomical cost . . . and further to the equally astronomical annual operating deficits now and in the future."

The only applause during Godwin's speech came in response to a mention of his resistance to federal requests to increase minority enrollments at the state's colleges and the number of white students at traditionally black schools. "I made it clear that Virginia during my administration would not submit to quotas by whatever name they might be called," he said to a light round of applause from some delegates.

That was but one of several references he made to the federal government.

At one point, he said that federal and state environmental "concerns" have delayed approval of highway projects, leaving $113 million in highway construction money lying idle. At another, he warned of "the stealthy spread of federal grants," which he said pay for some 14,000 state employees wholly or in part.

In the closing moments of his speech, Godwin said the legislators should learn a "lesson" from the last election. ". . . the people of Virginia expressed their inner feelings that the guilding principles of Virginia's government should not materially change . . ." he said, and closed with these words:

"And now with some measure of relief, and in all honesty, with a tinge of regret, I take my official leave of you, believing my duty done, my charge fulfilled.