President Carter proposed yesterday that funding for the National Endowment for the Arts be increased $26.1 million to $149.6 million in the next fiscal year, and the National Endowment for the Humanities rise to $145.6 million, up $24.6 million.

In the cover message that accompanied his federal budget, President Carter said that "emphasis will be placed on reaching underserved populations," in using the increased expenditures. Most grants are matched by contributions from non-federal sources.

Singled out for special mention in the budget message was a new Humanities Endowment program "in social history to increase public awareness and appreciation of the history of everyday life in America in the 19th and 20th centuries."

These increases would not be the largest percentage in the histories of the agencies, but they would be the largest in dollars. The Endowments, which started with minuscule budgets 13 years ago, have had their spending doubled in successive years on several occasions.

One arts agency now going into its second year, the Institute for Museum Services in the Department of Health, Education and Welfare, would have its spending nearly doubled under the budget proposal - from $4 million to $7.75 million. The Institute gives operatating funds for a wide range of museum services - from painting galleries to zoos.

In the Arts Endowment proposal, the largest increase would come in the regular programs, where standard grants go to individuals and institutions. This category, which accounts for two-thirds of the Endowment's spending, would go up by $13 million. The increase would allow the block grants that go on a matching basis to state arts agencies to increase from about $25,000 to $278,880.

The new challenge-grant program, under which matching grants are made on a 3-to-1 basis to arts institutions, would be increased from $18 million to $20 million. This year, the program's first grants went to 55 applicants out of approximatley 400. These grants are made on a one-time only basis.

The Humanities Endowment would receive an equivalent rise in program grant funds, with similar sums for state agencies. Its challenge-grant funds would go up by $9.5 million.

Other cultural items in the budget included:

Smithsonian Institution: up $8 million to $130 million.

Park Service maintenance expenses at the Kennedy Center: raised to $4 million from $3.75 million.