House-Senate budget conferees, taking a respite from taxes and defense, nibbled at domestic spending problems yesterday and explored a new way to finesse multibillion-dollar differences over recession relief.

Although most of their big problems remained unresolved, the chairmen of the two budget committees, Sen. Pete V. Domenici (R-N.M.) and Rep. James R. Jones (D-Okla.), said they thought the conference on the fiercely contested budget for fiscal 1984 was going better than they had expected.

As of late yesterday, when they recessed for the weekend, the conferees had given preliminary approval to domestic spending levels that exceed President Reagan's request by nearly $5 billion for programs ranging from agriculture to transportation. The only cut from Reagan's request came in projected spending on veterans.

But the most controversial areas of the budget remain to be completed, including the big social welfare programs that Reagan has targeted for retrenchment.

At least tentatively, the conferees were laying aside up to $11 billion in new and rejuvenated programs approved by the House for jobs and other recession relief and putting these amounts in a contingency "pool" that may or may not count in calculating the deficit.

Funds for these programs, which include public service jobs, relief from home and farm foreclosures and health insurance for the unemployed, would be included in the budget only if legislation authorizing the programs is approved by Congress.

In theory, this might satisfy liberals by allowing room for the spending but placate conservatives by denying use of the funds for anything else. However, some Democrats seemed leery of the approach, and the conferees reached no decision on how much money, if any, to put in the fund. On domestic spending in general, the Democratic-controlled House has proposed $16.4 billion more than the Republican Senate.

The House exceeded Reagan's domestic spending request by $29.2 billion; the Senate by $12.8 billion.

On the budget categories they had finished yesterday, the conferees settled somewhat closer to the figures proposed by the Senate than to those recommended by the House.

But the Senate conferees were in no mood for a simple split-the-difference solution that was proposed after a lunch break by the House Democrats.

"I can't believe it's a serious proposal," protested Domenici, who was joined by the ranking Democrat on the Senate committee, Sen. Lawton Chiles (Fla.) in opposing the idea.

Although other more liberal Senate Democrats supported the House proposal, Chiles gently reminded the House Democrats that the Senate budget was a bipartisan compromise, enacted with Democratic help only after Republicans could not unite behind a budget of their own. A split down the middle would scare off so many Republicans it could not pass the Senate, Chiles said.

Rep. Stephen J. Solarz (D-N.Y.) withdrew the proposal, but noted, "I have a feeling that before this conference is over we may yet snatch this proposal from the ether . . . to save this conference from collapse."

While the budget sets only tax and spending targets, it will be the framework for legislation that, because of the delay in passing the budget, is already beginning to move through Congress.

Reagan, who opposes both the House and Senate versions and is expected to find no comfort in a compromise between them, has vowed to veto any tax and spending bills that he regards as excessive.