President Reagan will propose some tax increases in 1983 and 1984 after all, and probably seek to raise more than the $22 billion over three years that he mentioned last September, Treasury Secretary Donald T. Regan said yesterday.

The secretary also said that, given the tax increases and additional nondefense spending cuts the administration will propose, federal budget deficits in both years will be "much lower" than $100 billion. Another high administration official said the estimate for the current fiscal year would also be less than $100 billion. Earlier estimates had suggested that the deficits would be more than $100 billion in all three years.

Regan stressed that the administration will propose no changes in the 25 percent personal income tax cuts passed last year. He also said, in an interview on NBC's "Today" show: "There will be nothing in 1982 in the way of tax increases." And he emphasized, as did a White House spokesman later, that the president has yet to make up his mind whether to seek an increase in excess of $22 billion in the subsequent years.

Regan said, "As far as '83 and '84, when the economy is better, I think there will be increased taxes. We've already discussed $22 billion worth in the proposals we sent up in September that were not enacted."

Those proposals were only spelled out in general terms; they were mostly relatively minor examples of what the White House has since called loophole closing. As to further increases, "We haven't even shown Reagan yet some of the things that we're considering in the budget area," Regan said.

Deputy White House press secretary Larry Speakes agreed that no decisions have been made on the tax issue and he refused to predict the outcome of the final budget decisions being made today and tomorrow by the president. "Nobody knows except the man in the Oval Office," Speakes declared, adding that the president "doesn't look with favor on new taxes."

In December, the president said at a news conference that he had "no plans for increasing taxes in any way." Minutes after the news conference, however, Speakes said that Reagan did not mean to rule out the kind of tax proposal he made in September--and since then various Reagan advisers have come to agree that he might have to propose more.

One set of administration estimates that became public last month showed budget deficits of more than $150 billion in 1983 and 1984 unless more spending cuts were made and taxes raised. Since then administration economists have changed their economic assumptions somewhat--principally to show inflation coming down a bit more slowly--in ways that tended to reduce the deficits.

Now, with the additional assumption that the president will go along with a variety of higher taxes, such as increased excise levies on alcohol, beer, wine and possibly gasoline, Reagan's advisers have been able on paper to hold the deficit below $100 billion each year. Moreover, one adviser said, it will be shown declining each year.

The Treasury secretary also confirmed reports that defense spending would be going up about 15 percent in the 1983 budget, while additional cuts would be made in programs such as Medicaid and child nutrition. Regan called the defense increases "fair" and said they are needed because "the defense posture of the United States has to be built up."

As for the nondefense programs, he said, "We're keeping the nucleus of the programs for what they were designed in order to help those people who need Medicaid and the like. But what we're trying to do is to eliminate the growth that there has been in Medicaid over the last several years. These programs have grown enormously, and there's no need for that."