President Reagan said at his news conference yesterday that he has "no plans for increasing taxes in any way" to help reduce the large budget deficits his advisers say may otherwise occur over the next several years.

The president's Office of Management and Budget has forecast that the deficit will be above $150 billion in both the next two fiscal years if no further steps are taken, and experts both in and outside the administration have said there is no way to reduce these likely numbers to acceptable levels without tax increases as well as spending cuts.

The president's remark would thus commit him to seek even larger additional spending cuts in his next budget than had been expected, or tolerate much higher deficits.

Reagan also indicated strong support yesterday for early deregulation of natural gas prices, and challenged estimates that this could cause them to double or triple.

The administration is still considering whether to propose that controls be lifted from natural gas faster than provided under current law; several senior officials have suggested linking such a speed-up with a new tax which could raise $10 billion to $20 billion a year.

However, Reagan ruled out this potential revenue raiser, saying "my consideration of the decontrol of natural gas is on decontrol only," when asked about a possible new tax.

The president's rejection of tax increases was met with surprise and some dismay among budget experts yesterday. A senior Republican staff member in the Senate commented that "responsible people" there were assuming that there had to be $25 billion to $30 billion of tax increases to keep the deficit in bounds for fiscal 1984, with somewhat smaller increases in 1983.

Congress would have to vote these increases in an election year and in the midst of a recession. And "without presidential leadership you can't do it," the staff member said.

Administration officials themselves seemed to be caught partly by surprise by the president's remarks, and suggested a tax increase still might be forthcoming.

One aide said the president had not focused on tax possibilities yet in deciding on next year's budget. Deputy press secretary Larry Speakes said the president might yet propose some tax "loophole pluggers" that would raise some revenue; he refused to speculate how much.

Within the administration there is a split between those supply-siders who believe that the deficit is not as important as holding down taxes, and others who think the deficit must be reduced as the economy begins to recover next year. One in the latter camp commented yesterday, "the ball game isn't over yet."

OMB Director David A. Stockman was in the forefront of those arguing for some tax increases but since embarrassing remarks of his were quoted in a magazine article last month he has concentrated on the battle to hold down spending, administration sources said.

However, "nobody really knows how much juice there is" to be squeezed out of the spending side, one official commented yesterday. If the cuts agreed to by the president still leave large deficits, "those of us who think it is important to have the deficit declining when the economy recovers" will present that to the president, he added.

However, Reagan backed off much further yesterday from any commitment to reduce the expected budget deficits within a certain time. He said he did not believe policy should be aimed at hitting a particular deficit number, as long as the paths of spending and revenues were converging. With no new proposals the deficit is now set to increase substantially.

Throughout his political career Reagan has stressed the connection between budget deficits and inflation. He said earlier this year that "we know inflation results from all that deficit spending" and predicted a balanced budget by 1984.

However, the president said yesterday he did not "believe anyone can make a proper estimate" of future deficits. He refused to say directly what size deficit he would find acceptable, telling reporters that policy was aimed at eliminating "every bit of unnecessary spending that you can" but should not involve "just single-minded pursuit of reducing the deficit" which might leave "government being irresponsible and not performing the services that it is supposed to perform for the people."

The president is now in the middle of reviewing the budget and hearing the appeals of agency heads who do not want to accept all the deep new cuts suggested by Stockman. But his senior advisers have yet to agree on a new economic forecast, on which the final budget numbers will be based. The gloomy deficit projections leaked last week were based on forecasts by Reagan's Council of Economic Advisers, headed by Murray L. Weidenbaum.