When he was running for governor of Virginia. Democrat Henry E. Howell promised he would come to Washington often after the election, but "not to look at the monuments."

Yesterday Howell, who was defeated Nov. 8 by Republican John N. Dalton, made good on his campaign promise, paying what a White House official later called "a personal visit" on President Carter.

Howell and White House officials described the visit as more social than political and said the possibility of Carter naming Howell, a longtime friend, to a federal job was not discussed.

"I just think the President wanted to make me feel good," Howell said after his 15-minute meeting with Carter in the Oval Office yesterday morning. "We just talked generally about politics in Virginia . . . nothing specific."

Howell said he told the President "I stood ready to help the administration in any way I could," but said his immediate goal is to "re-establish my law practice."

Howell, 57, a Norfolk lawyer, often expressed disdain about taking a job with the federal bureaucracy during his election campaign.

Recently he told a Norfolk newspaper reporter he "might be interested in appointment to a federal appeals court at some time in the future.

But deputy White House press secretary Rex Granum said after the meeting that there as "no offer" of a federal job and that he was not aware of any appointment pending for Howell. Howell was the first major Democrat in Virginia to support Carter's bid for the presidency. During his campaign Howell told voters "my friend across the Potomac" would be a valuable resource for the state.

Howell's Norfolk associates say they expect Howell will remain in his law practice there and begin paying off the $65,000 debt left from the campaign, is third race for governor. His wife Elizabeth, has begun her campaign for re-election to the Norfolk City Council this spring and that race is expected to place pressure on Howell to stay in Norfolk, friends say.

"It's always an honor to listen to the President," Howell said this week in explaining why he was visiting Carter. Carter had suggested they meet when he called Howell on the night of Howell's defeat, White House officials said.

Howell's contended he is more interested in Virginia politics than national politics. Yesterday, as he left the White House with his daughter, Mary, he told reporters he believes Virginia Democrats should nominate their candidate for Senate next year in a convention rather than through a primary.