The Democrat-dominated Virginia House of Delegates approved a Republican-sponsored resolution today urging President Carter not to grant a "blanket pardon" to Vietnam-era military deserters.

Heavily amended from the Republicans' initial resolution that would have condemned Carter's plans - as the legislators once understood them - to grant pardons to both "draft dodgers and deserters," the measure passed the House on a 52-to-29 vote with virtually no debate.

Del. George W. Jones (R-Chesterfield), chief patron of the resolution, appeared to have ended any prospect of debate when he assured the House that the measure did "not in anyway address" what Carter did Jan. 21 in pardoning Vietnam era draft evaders or resisters. On that day the President asked the Defense Department for recommendations on what he should do about military deserters, which Jones said was the only issue addressed in the resolution.

The resolution is only advisory and will be sent to the State Senate for further consideration. If the Senate approves, it will be forwarded to the President and Virginia's congressional delegation.

In other action, the House gave final approval to two controversial measures and sent them to the Senate. By a vote of 63 to 31, the House gave final approval to a bill that would end Virginia's six-year ban on annexations and by a 73 to 15 margin approved a bill that would somewhat liberalize the state's current restrictions on branch banking.

Northern Virginia's delegation was divided over the annexation bill. Four Fairfax Republican delegates - Warren E. Barry, Wyatt B. Durrette, James H. Dillard, and Robert E. Harris - and Fairfax Democrat Thomas J. Rothrock voted against the measure, which had initially passed last night on a voice vote. All other Northern Virginians voted for the bill, which could result in some suburban counties paying funds to older, central cities.

The branch banking bill approved by the House is substantially weaker than the measure sought by the State Corporation Commission and some large bank holding companies that wanted legislation allowing statewide branching.

Under the bill, banks that are currently restricted to banking in one county would be allowed to expand into adjoining counties.

The measure would not affect national banks, regulated by the federal government, and some banking organizations that have through acquisitions, in effect, managed to develop statewide banking, supporters of the measure said.

On the Senate floor today, Sen. J. Marshall Coleman (R-Staunton) again complained that the Democratic caucus of the legislature plays too important a role in the selection of state judges by effectively eliminating debate on the Senate floor. His attack brought Sen. William F. Parkerson (D-Henrico) to his feet, claiming that Coleman's remarks would probably hurt chanced for revival of a bill that would create a commission to advise the legislature on judicial selections.

The measure, sponsored by Parkerson, died Tuesday by a 19-to-20 vote, but was returned yesterday to the Senate Courts of Justice Committee so it might be amended to overcome some of the objections it encountered on the Senate floor.