Leaders of Congress' two taxwriting committees met yesterday to discuss a possible compromise on President Reagan's tax-cut plan, but apparently made little initial progress.

At the end of the hour-long luncheon, Sen. Bob Dole (R-Kan.), chairman of the Senate Finance Committee, said the four were now "in the same ball park," but had not agreed on any specifics.

Nevertheless, the session -- the first time the four had met privately for such talks -- was looked on as an important step toward eventual enactment of the bill.

The leaders are expected to meet, possibly this week, with Treasury Secretary Donald T. Regan, who cut short an overseas trip to return for the discussions. Sources said the negotiations would go on for another week or two.

The administration has proposed a 10 percent across-the-board cut in income tax rates for each of the next three years, but congressional Democrats -- and some Republicans as well -- are balking at the plan as inflationary and for other reasons.

Last week the White House, after standing firm for almost three months, signaled to the tax-writing chairmen that it finally was willing to explore a possible compromise on the president's plan.

Besides Dole, the four yesterday included House Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.), and Sen. Russell B. Long (D-La.) and Rep. Barber B. Conable (R-N.Y.), ranking minority members of the panels.

Conable told reporters after the lunch session that after an initial discussion, the four "agree on what the problems are." Conable said the leaders discussed "the nature of the options that need to be considered."

However, sources said Rostenkowski, who is a key to any House-Senate compromise, still has not softened his opposition to enacting a tax cut for more than one year -- one of the features Reagan considers most important.

Dole told reporters yesterday he saw no outline of a compromise that could emerge from yesterday's session. "If we're really sincere about a bipartisan effort, the next move should be from Danny [Rostenkowski,"] he said.

Besides the question of whether the tax cut is "multi-year," other issues to be resolved are how large the overall tax cut should be and how many other amendments members should be allowed to tack on.

The White House, which is trying to keep the tax bill free of members' amendments to ward off any erosion of Reagan's own program, has promised to propose a second tax bill in August, but many lawmakers are skeptical a second bill can go forward.

Yesterday, assistant Senate majority leader Ted Stevens (R-Alaska) told reporters there is limited support for the full Reagan plan and predicted the Senate would go along with whatever the Finance Committee recommends.

Rostenkowski has proposed an alternative tax plan that would scrap Reagan's three-year cut and substitute a one-time cut in the top tax rate for investment income, elimination of the "marriage penalty" and various savings incentives.

The Ways and Means Committee tentatively is scheduled to begin formal markup of the tax bill May 28, while the Finance Committee is expected to start drafting its own version early in June.

The move toward compromise came after it became apparent that there were not enough votes on either tax-writing panel to pass Reagan's plan intact. None of the four at yesterday's lunch is enthusiastic about the Reagan proposal.

Reagan, however, still is fighting hard for a multi-year tax cut. On Sunday, after Dole talked of compromise during a television appearance, the president telephoned him personally to reaffirm his insistence on that feature.