Treasury Secretary Donald T. Regan is studying the need for further tax increases to fight the huge federal deficits projected for years to come, a Treasury spokesman said yesterday.

Regan, a former Wall Street financier, is particularly worried that the prospect of continued high deficits will upset financial markets and keep interest rates high, according to spokesman Marlin Fitzwater.

Regan, however, has not talked to President Reagan about the possibility of new tax increases and would prefer to reduce deficits without any, Fitzwater said.

The president, asked yesterday about reports that Regan is arguing for tax increases, said, "Don't believe everything you read in the papers." Deputy White House press secretary Larry Speakes, traveling with the president to Arizona, told reporters, "Wait and see when the budget comes out."

The budget for the 1984 fiscal year, begining next October, is scheduled to be published late next month. "I wouldn't look for any substantial new taxes," Speakes said, although he refused to rule out higher taxes.

Several officials believe that without some tax increases it will be impossible to make significant inroads on deficits predicted to range as high as $200 billion for 1984. Some officials also privately say there should be a scaling back of the president's planned defense buildup.

Regan generally has been one of the administration's most ardent opponents of tax increases to help cut deficits, although he did support last summer's $98 billion tax-increase bill. Just a few weeks ago Regan was in favor of bringing forward next July's income tax cut to January. Since then, however, he has become more concerned about the deficits that are projected for the years after 1984, Fitzwater said.

Although Regan has not advocated any specific proposals for tax increases, the kinds he might favor include abolishing the interest deduction for mortgage payments on second homes and limiting the deductions for interest on consumer debt, excluding auto purchases.

Neither of these measures would raise much money, Fitzwater acknowleged.

The administration has agreed broadly on an economic forecast that shows only slow growth next year, sources said. A weak recovery tends to make the deficits larger by reducing tax revenues. Administration forecasts have been widely criticized in the past for being far too optimistic about growth and deficits.

The current forecast is "certainly more consistent with the private forecasters' consensus than Reagan administration forecasts were previously," a spokesman for the Council of Economic Advisers said yesterday. The average forecast among leading private economists is for less than 3 percent real growth next year.

In considering proposals for higher taxes, Regan also is attempting to head off proposals that have been coming in from all sides during the budget negotiations, a Treasury official said.

Instead of proposing new spending programs, which runs against administration policy, departments are thinking up tax measures that would help to promote certain activities, he said. The Department of Education has proposed tax-sheltered savings accounts, similar to those available for retirement savings, in which people can save for sending children to college.

One proposal -- a plan to tax employes on health insurance premiums paid by employers -- would actually raise revenue, while others would create new tax loopholes.

The Commerce Department has also suggested various new tax measures to aid business, Fitzwater said.

This fall, the president said it would take a "palace coup" to get White House support for tax increases next year. But shortly afterward he backed a 5-cent increase in the gasoline tax, effective April, 1983. It has been approved by Congress.