Henry E. Howell, Democratic candidate for governor of Virginia, came away from a meeting with President Carter yesterday predicting that Carter will make a campaign trip into Virginia on his behalf this fall.

After having lunch with the President in the Oval Office, Howell said "The timing will depend on his commitments and his great responsibilities." Howell said later that he would expect Carter to make only one campaign appearance in his behalf.

Earlier, in an appearance with Howell in the White House Rose Garden, the President pledged his full suppott of the Democratic candidate but made no specific promise of a campaign appearance.

"I don't know about campaigning - whether we'll be able to go from country store to country store," Carter said. "But there is no doubt about it that as the Democratic nominee, he will have our complete support."

The President's remark referred to a Howell campaign practice of visiting dozens of small stores in motor home tours of rural Virginia.

The White House visit by Howell, his wife, Elizabeth M., their three children and members of Howell's staff was the result of an invitation issued by the President on June 14, the day Howell defeated former Virginia Attorney General Andrew P. Miller in the Democratic gubernatorial primary.

Howell was an early and strong supporter of Carter's bid for the Democratic presidential nomination. During the Virginia primary he often recalled that Carter had slept in Howell's bed when he visited the Howell family in Norfolk.

Carter stayed out of the primary, but it was apparent that the Carter family and members of his old campaing staff favored Howell. One of the President's sons, Jack, spent three days campaigning for Howell.

There is no unanimous opinion among campaign officials on how much help Carter might be to Howell in his race against Republican Lt. Gov. John N. Dalton. Presidents have a mixed record in their attempts to affect the outcome of state elections.

However, in 1969, the combination of a personal appearance and election-eve television appeal by President Nixon was thought to have made a major contribution to the decisive victory in Virginia of former Republican Gov. Linwood Holton over Democrat William C. Battle.

Before the luncheon with President Carter, Howell met with U.S. Commissioner of Education Ernest Boyer to discuss federal impact school aid and federal aid to education of handicapped persons and then went to Democratic National Committee headquarters to talk about the possibility of party assistance in the coming race.

National Chairman Kenneth Curtis told Howell in front of reporters, "Whatever resources we have are at your disposal," The national party, however, has substantial debts and Howell said later that he expects the DNC to be helpful primarily in improving our communications techniques."

Harris remained neutral in the primary but has been as Howell supporter and now serves as chairman of the campaign coordinating committee providing liaison between Howell and his running mates, Charles S. Robb for lieutenant governor and Edward E. Lane for attorney general.

At the White House, Howell also met with presidential aides Hamilton Jordan and Timothy G. Smith. Smith was Carter's campaign coordinator in Virginia, where the President was narrowly defeated by former President Ford. Smith now is deputy appointments secretary at the White House.

Howell said Smith would serve as liaison between him and the White House at least temporarily. "Tim Smith will be our man in Washington, for the time being," he said.

Some of Howell's White House visit was taken up with exchanges with the press.

He praised Carter for "affording leadership," restoring belief in human rights, holding out the promise of greater consumer protection and "having the nerve to say we don't need all these dams."

A few minutes after this reference to the White House scrutiny of water projects already approved by Congress, Howell announced that the administration has given approval for completion of a $7 million, multiagency flood control and housing project on the Clinch River in Wise County in Southwest Virginia.

Howell said he had worked for completion of the project and seemed to offer it as an example of how he - more than a Republican - can help Virginia in dealing with this administration. He acknowledged, however, that it was a Carter administration reappraisal that put the Wise County project in jeopardy in the first place, making the rescue by Howell and others necessary.

Howell was asked several times yesterday by national reporters for his position on the B-1 bomber, a controversial new plane up for final approval by Carter.

"I really haven't had the staff to work on it," he said airily. Then, referring to the five-place, single-engine Mooney Mustang that often serves as his campaign plane, he added.

"All I worry about in that area is the Mooney that broughtme up here today."