Despite high unemployment during the fall and winter campaign period, charitable contributions to United Way drives throughout the country rose 10.3 percent, officials reported yesterday. The metropolitan Washington drive showed one of the largest corporate-giving gains among big cities.

A record $1.68 billion was raised nationwide, the most by the United Way movement in its 95-year history..

In the Washington area, the recent fund drive raised a record $28.7 million, up $2.8 million from the previous year.

The highest percentage increases came from the West, Chairman Donald V. Seibert said at a news conference here. Citing individual generosity in difficult times, Seibert said there has been no such dramatic increase in giving since 1931.

Individual contributions constitute 68 percent of United Way giving, with an additional 28 percent coming from business, 2 percent from foundations and 2 percent from other sources. United Way organizations in 2,100 communities channel these funds to various nonprofit groups in local areas.

Denver, Houston, Dallas and Washington provided the greatest increases in business sector contributions, which were up on a national basis by 10 percent. Seibert, who is chairman of the J. C. Penney Co. retail chain, said he is optimistic that business and corporate contributions will continue to increase, although he conceded there is no way business, foundation and individual giving can match the level of federal tax dollars no longer available for human services.

The administration has called repeatedly for private giving to fill the gap created by federal budget cuts, and Seibert said: "We will all have to learn how to work more effectively with less resources available . . . Our system is based on looking for money coming into the community and seeing where the local groups already are getting money."

However, the Conference Board, a nonprofit business research organization, recently conducted a survey of 400 large companies and learned that while 60 percent of the companies plan normal increases in their contributions budgets in 1982, only 6 percent are lifting their budgets in response to government cuts.

On a more immediate and short-term basis, United Way announced yesterday a community transition fund involving the public and private sectors is being established to assist temporarily people severely hurt by budget cuts. The transition fund seeks to raise $1 million by April 1982..

United Way also said a Hispanic leadership development program will be undertaken to strengthen the managerial skills of the nation's Hispanic community-service agencies.