Pressure is mounting for Democratic Gov. Charles S. Robb to name the first black to the Virginia Supreme Court when he fills a vacancy left open at the end of this year's General Assembly session.

Civil rights groups and black leaders around the state are urging Robb to take advantage of an opportunity to break the all-white membership on the state's high court and to affirm his pledge for greater black representation throughout state government.

"It will certainly mark a watershed. His actions on this appointment will send a signal of some significance to the black community," Del. William Robinson (D-Norfolk) said. "This is an opportunity for him to make an imprint on the judicial fabric of the Commonwealth. I think he has the courage; I hope he has the will."

At a press conference today, Robb announced he would make the Supreme Court appointment himself, which is his prerogative since House and Senate Democrats deadlocked over two nominees during the last weeks of the 1983 General Assembly session.

It is the first time in more than a decade that a governor has been able to fill a vacancy on the seven-member court. But he dodged questions on whether he would give special consideration to qualified black candidates.

"I am going to start from a clean slate," said Robb, who was elected with strong black support. "It is now my responsibility."

The legislature's two candidates--Circuit Judges Marvin Cole of Richmond and William Hodges of Chesapeake--are "neither definitely in nor definitely out," said Robb, who would not predict how soon he would make the appointment.

Some black legislators said the Supreme Court vacancy gives Robb a chance to make up for his lukewarm support of a bill to declare a Martin Luther King holiday in Virginia that died this year in a House committee.

"Given the lackluster performance this session, this would go a long ways towards atoning in the minds of some for his less than complete commitment to the passage of the King bill," said Robinson, one of five black state legislators. "The King holiday was a symbolic gesture; this is something of a more substantive nature."

Robinson has written Robb to urge the appointment of a black Supreme Court judge; so has the state NAACP chapter and the Virginia unit of the Southern Christian Leadership Conference.

"This is an opportune time for Robb to transform his words and visions for a progressive Virginia into a small piece of reality," said Jack Gravely, NAACP executive director.

Sen. L. Douglas Wilder (D-Richmond), a key Robb adviser and ranking black leader in the state, supported Cole in the Senate Democratic caucus. That support remains unchanged, Wilder said today, unless somehow Cole is dropped from consideration.

In that event, Wilder said he will join other black leaders in winnowing through the list of qualified black candidates from around the state. "For those who say it is Richmond's time, we have them here. For those who say it is Tidewater's time, we have them there," said Wilder. "And for those who say it must be the most meritorious, we have them everywhere."

Wilder said the push for a black Supreme Court judge should not be linked to the King holiday or any other legislation. "Blacks feel they are entitled to both," he said. "There's no need for any quid pro quo."

The list of black judges and lawyers to be considered includes Arlington Circuit Court Judge Thomas Monroe, Richmond Circuit Court Judge James Sheffield, former Richmond mayor Henry Marsh III, several District Court judges and prominent black attorneys, Wilder and others said.

Robb said he would solicit opinions from key legislators and from state bar associations, including the Old Dominion Bar Association, a predominantly black organization whose president, Bobby Stafford, said today he would submit names to the governor in the next few days.