House Budget Committee Chairman William H. Gray III (D-Pa.), breaking out of the paralysis over tax increases that has gripped both parties, said yesterday that Congress should raise taxes to help reduce deficits after nailing down at least $50 billion in spending cuts for fiscal 1986.

In a further sign of renewed pressure for revenue increases to help control rising deficits, Senate Majority Leader Robert J. Dole (R-Kan.) held out the possibility of a small tax increase in connection with efforts to overhaul the tax code this year.

But House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) adamantly reasserted his insistence that President Reagan must abandon his opposition to tax increases before Democrats will take any initiative on the issue, saying they are tired of being "clobbered over the head" as "big taxers."

The comments from Gray and Dole, among the strongest so far from key players in the budget struggle on Capitol Hill, came as House-Senate negotiators opened what is expected to be a difficult conference over the two chambers' plans to cut $200 billion-plus annual deficits in half over the next three years.

Apparently eager to show momentum toward an agreement, the conferees decided a few relatively minor issues, leaving until later such potentially divisive big-ticket items as defense spending, inflation adjustments for Social Security benefits and other proposed cutbacks in domestic programs.

Speaking to a conference of the American Stock Exchange, Gray cited gloomy economic forecasts pointing to ever-higher deficits even as Congress is slashing spending to cut the deficits, and he said:

"Spending cuts alone will not do it. We will have to face the reality of dealing with some revenues in order to get deficits down faster and ensure economic growth and opportunity."

Referring to both administration and congressional estimates that deficits will remain well above $100 billion in fiscal 1988 even if all the proposed savings are made, he said, "You can't cut your way out of the debt that this administration has created fast enough. It cannot be done. We have to do more . . . . "

Noting that Reagan's continued opposition would make it "very, very difficult" to pass tax-increase legislation, Gray said he hoped the president would reverse course and support a tax increase if Congress approves at least $50 billion in spending cuts for next year. He suggested that revenue from such an increase be "dedicated" to deficit reduction.

Gray did not specify the type or size of the tax increase he had in mind but suggested that it might be included in tax-overhaul legislation that is expected to begin moving through Congress this fall.

Without specifically endorsing a tax increase, Dole suggested that if Congress could improve on deficit-reduction plans that were approved by the two houses it might then ask Reagan to consider a small tax increase.

Dole mentioned a tax increase of about $50 billion over five years, equivalent to 1 percent of federal revenues. Treasury Secretary James A. Baker III, under questioning from Dole at a Senate Finance Committee meeting, had indicated that the tax-overhaul plan could include a revenue gain or loss of about 1 percent and still be considered "revenue neutral."

Following Reagan's lead, Dole has held the line against tax increases except as a "last-resort" after all possible spending cuts are made. While $50 billion in new revenues over five years would hardly make a dent in deficits, Dole's suggestion appeared significant because it was the second day in a row that he suggested deficit-reduction moves that could result in tax increases.

On Monday he proposed including state and municipal employes under Social Security and Medicare, adding an estimated $8.3 billion in revenues over three years as they begin paying payroll taxes for the retirement and health benefits.

While O'Neill did not close the door on tax increases, he remained firm in insisting that Reagan take the lead. "We have a very formal and stern policy: Any tax increase is going to come after the president recommends it," he said.

Noting that Reagan has used previous tax increases supported by Democrats against them in campaigns, O'Neill said, "We're not going to be the big taxers he likes to portray us as being."

In a testy send-off for the conference, O'Neill and Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) clashed over the Senate's proposal for a one-year freeze of Social Security benefits.

At a mid-day news conference, O'Neill reasserted that Social Security was "off the table" as far as he was concerned and suggested that Senate conferees were ready to "run away from their proposed freeze as fast as they can."

In reference to O'Neill, Domenici said as the conference opened a few hours later, "I hope he is not serious when he hints that he would rather see us torpedo this entire budget conference over one issue, even if that issue is adjustments upward in pensions. We cannot jeopardize the well-being of more than 225 million Americans over any one part of the budget."

But O'Neill and Domenici signaled flexibility on other issues.

O'Neill indicated he could move toward phasing out some state and local aid programs, such as Urban Development Action Grants, and cut back some small-business programs.

Domenici suggested cracking down on programs such as Amtrak, export-import aid and federal retirement to protect social welfare programs and is expected to propose a compromise along these lines as a starting point for real negotiations.

In initial action yesterday, the conferees agreed to protect funding for the space station and provide for 800 more customs agents. The conference resumes today.