In a backhanded concession to the Reagan administration, the chairman of the House Ways and Means Committee yesterday agreed to add a third year to the Democratic tax bill if it is slanted to the middle class and contingent on major improvements in the economy.

Appearing on "Meet the Press" (NBC, WRC), Dan Rostenkowski (D-Ill.) effectively conceded that the House will approve a third year of tax cuts. The move is designed to attract southern Democrats and some northern Republicans who want to retain the appearance of loyalty to President Reagan. In addition, it focuses attention on what many believe are extremely optimistic economic projections by the administration.

An administration spokesman quickly rejected the Rostenkowski "compromise," declaring that "Rostenkowski wants to place the burden on us of achieving our economic targets using his tax bill. There is no way we can get to our targets using his bill."

The spokesman argued that by targeting the cuts to the poor and middle class, the Democrats are encouraging inflationary consumption instead of savings and investment, both of which Republicans contend will increase more through their bill because it provides larger cuts to the rich.

While not responding directly to Rostenkowski, Treasury Secretary Donald T. Regan, appearing on the Cable News Network show "Newsmaker-Sunday," attacked the triggering concept for a third-year tax cut as a mechanism to "hold the American people hostage for some event to occur."

The two key elements of the Rostenkowski proposal are that the third-year cuts are targeted toward persons making from $15,000 to $500,000, as in the Democratic bill for the first two years, and that the third year be contingent on achievement of three administration economic goals.

These goals ara a $23 billion deficit in 1983, lowering of the average inflation rate from 1981 through mid-1983 to 7.5 percent and reduction of the rate of interest on three-month Treasury bills to 7.5 percent in 1983. (Last week the average yield was 14.558 percent.)

Pointing out that these figures are based on the administration's own targets contained in the midyear economic review, Rostenkowski said, "If this administration is committed to their economic forcasts, to what they see as the need for a third year, Dan Rostenkowski would try to use his influence" to get the House leadership to back his proposal.

Just as Democrats are moving to solidify support among southern colleagues and possibly some Republicans, administration sources said there is a growing likelihood the GOP bill on the Senate floor will be sweetened with additional tax breaks for oil producers.

The Senate bill already calls for progressive reduction of the rate of the windfall profits tax on "new" oil from 30 percent to 15 percent by 1986. Sources said this is likely to be lowered even further to either 10 percent or down to zero. Lowering the rate from 15 percent to zero would cost, according to rough estimates, another $1.5 billion.

Administration sources are nowhere near as confident of winning on the House floor on the tax bill as they were at parallel points in the two previous budget fights and, they are quick to acknowledge, the margin of victory in the last major House floor vote was only 7 votes, 217 to 210.

Adding the larger oil tax break, a move expected early this week on the Senate floor, is expected to attract Democrats from oil states. In the last budget vote, 29 Democrats defected to the Reagan administration, and nine were from Texas.

House Democrats have not yet agreed on oil tax provisions in their bill, although they have considered exempting up to 1,000 barrels of oil, old and new, from the windfall profits tax. The exemption would be phased in, but when fully in place would be very expensive, costing in the range of $4 billion in lost revenues annually.

Rostenkowski admits being in a bidding war in the Reagan administration on the tax bill, but, largely because of the cost, the likelihood that the Democratic bill would go farther in the area of breaks for oil than the Senate GOP bill has declined significantly.

Ways and Means Committee aides said yesterday that in accepting a third year of tax cuts, Rostenkowski raised the danger of losing support for his bill from House liberals, many of whom argue that the administration's tax package is a back-door way to force a steady reduction of federal revenues and consequently increase pressure to cut social programs.

In terms of developing a trigger mechanism for the third year of the tax cut starting July 1, 1983, committee aides said there would be no problem determining the rate of interest on Treasury bills and the average inflation rate, but they acknowledged that the deficit figure for 1983 would be impossible to obtain, because the fiscal year does not end until Sept. 30, 1983.