House Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.) agreed informally yesterday to begin exploring a possible compromise on President Reagan's taxcut plan, ending an impasse that had threatened to stall the bill.

The decision came during a 1 1/2-hour meeting with Treasury Secretary Donald T. Regan. Both sides stressed that no deals had been struck, and the two are still far apart, particularly over how many years the cuts should continue.

Rostenkowski's new willingness to go ahead with talks came after Reagan made overtures to conservative southern Democrats on the possibility of another GOP-Dixie coalition similar to the one Reagan used to win his budget fight.

Yesterday's meeting climaxed three weeks of political sparring over which side would propose compromise talks first, the administration or Rostenkowski. Each had contended it was waiting for an invitation from the other.

In the wake of yesterday's session, the Ways and Means chairman scheduled a round of discussions with key congressional figures, including another meeting next Wednesday with Senate Finance Committee chairman Robert Dole (R-Kan.).

Dole, Rostenkowski and the ranking minority members of the two tax-writing panels met on Monday to discuss a possible compromise move, but the Ways and Means chairman was noncommittal pending talks with House Democratic leaders.

The Ways and Means chairman also has called a caucus of committee Democrats for this coming Thursday, presumably to sound them out on strategy. Most of the panel's Democrats so far have opposed the president's plan.

Although yesterday's session with Reagan did not break any new ground on the substance of any compromise, it did get the negotiations going in earnest. Republican leaders had feared any further delays might doom the whole effort.

Rep. Barber B. Conable (R-N.Y.), ranking minority member of the Ways and Means panel and an instrumental figure in the talks, said yesterday's developments showed "We have a lot of action, but there still is no movement." d

Reagan has proposed a 10 percent-a-year cut in tax rates for each of three years, with 5 percent to take effect July 1, two more 10 percent cuts in January 1982 and 1983 and a final 5 percent in January 1984.

On Wednesday, Reagan had hinted to southerners that the adminstration might be willing to postpone the current year's cut to Oct. 1, to help hold down the fiscal 1982 budget deficit, and consider Democrats' proposals as well.

Yesterday, however, the Treasury secretary stressed in a telephone interview that the administration will still in the process of exploring other alternatives and is "not on the verge of making a compromise."

"So far, it is a lot of conversation," Reagan said.

The secretary also reitereated that Reagan's insistence on a "multi-year" tax cut "is not negotiable. We have to have a multi-year bill," he said. "The president was elected on that basis. There can be no give on that point."

Regan said he had "urged speed on" Rostenkowski in yesterday's talks, adding: "We have one eye on the calendar." He also contended the administration had gained by standing firm: "[The Democrats] are coming a lot closer to us."

Sources close to Rostenkowski indicated the chairman still has not abandoned his insistence that the tax cut be confined to one year. However, most onlookers expect any compromise to involve a two- or three-year cut.

The two men also discussed the possibility of considering other tax-cut proposals that are being pushed by individual House and Senate Democrats. However, Regan still wants to defer these to a second bill later this year.

Meanwhile, southern Democrats who met with Regan on Wednesday took pains to make clear yesterday they still intend to work with Rostenkowski and not bolt to a Dixie-GOP substitute, as they did on this month's budget fight.

Rep. G.V. (Sonny) Montgomery (D-Miss.), one of four southerners at the Regan session Wednesday, said the conservatives "still are Democrats, and if we could go the Democratic route, that's what we'd like."