Virginia Democratic Gov. Charles S. Robb said today he had held private meetings with the party's two candidates for governor amid indications that party leaders are suggesting Lt. Gov. Richard J. Davis withdraw from the race.

Robb has remained publicly neutral in the contest, which state Attorney General Gerald L. Baliles apparently won Monday, the second of two days of delegate selection caucuses across the state.

Virginia Democratic Party Chairman Alan A. Diamonstein added to the speculation that officials want Davis to concede by saying today that the Democrats should not "allow ourselves to get into a childish attitude like that expressed by the Republicans."

He was referring to Rep. Stan Parris, the Northern Virginia congressman who has said he will continue to seek the GOP nomination for governor, even though Richmond lawyer Wyatt B. Durrette apparently won that race this week.

Diamonstein said that he did not believe Davis "will allow it to go to a convention battle," unless there is "an obvious" chance for him to overtake Baliles. The party chairman said he is neutral and would not speculate on Davis' chances.

Today's developments appeared to be the latest signs that Baliles, 44, is trying to consolidate his support and force Davis out of the race without embarrassing the 63-year-old lieutenant governor. Davis had been considered the front-runner for much of the past year.

Baliles' campaign advisers refused to characterize their candidate's meeting with Robb. David Doak, Baliles' chief campaign consultant, called the Baliles-Davis situation "too delicate" to discuss.

George M. Stoddart, Robb's press secretary, said Robb met with the candidates separately Wednesday for "private conversations" initiated by them. "They talked about the nomination" and time left before the party's June 7 convention in Richmond, Stoddart said. He declined to elaborate.

Ken Storey, Davis' press secretary, said Davis met with Robb "to go over the delegate numbers . . . and explain how Davis is going to win." Storey said the possibility that Davis might abandon his planned challenges to Baliles delegates "was never brought up."

Leaders of the Davis campaign, including senior fund-raisers, were meeting at an undisclosed site in Tidewater today. Storey said the meeting was to "map strategy" for the "next nine weeks of the campaign."

According to the party, Baliles has won 1,680 delegates at the caucuses, while Davis has 1,586, and 189 are uncommitted. Baliles since has claimed the support of 104 of those uncommitted delegates, as well as 48 state legislators who are convention delegates. This gives him more than the 1,803 votes needed for nomination.

Davis is claiming the support of 33 automatic and 29 uncommitted delegates, which leaves him short. He can win only if he successfully challenges Baliles' delegates.

Storey said the Davis campaign is prepared to challenge 73 delegates and may go after as many as 200 of the Baliles delegates. Baliles is considering a delegate challenge of his own that could add 80 delegates from Hampton to his total.

Aides to Davis and Baliles say the men are continuing to call delegates and party leaders in an effort to shore up their positions.

Diamonstein, who said he will not seek another term as head of the party, said the competition could be healthy for the party if it does not continue too long.