The Carter administration asked the Senate yesterday to make major changes in the tax bill the House passed last week, but - in a new anti-inflation gesture - urged senators not to enlarge the size of the overall tax cut.

Testifying before the Senate Finance Committee, Treasury Secretary W. Michael Blumenthal warned that increasing the tax cut beyond the $16.3 billion voted by the House would "create serious risks" of new inflation and possible recession.

At the same time, Blumenthal withdrew the administration's previous opposition to a reduction in capital gains taxes, saying the White House would accept a capital gains cut "if it meets the criteria we set out."

Officials said the $16.3 billion House bill actually was close to Carter's own target of a $19.4 billion tax cut, after taking account of differences in estimating procedures between Congress and the Treasury.

Even so, initial indications were that the administration might not get its way. Sen. Russell B. Long (D-La.), the Finance Committee's chairman, reiterated his intention to enlarge the cuts if the budget allows.

Meanwhile, Carter told a news conference yesterday he would have "no hesitation in vetoing the tax bill" if the Senate does not make the "basic changes" he is seeking. "I am not satisfied with the bill the House has passed," he said.

The changes Blumenthal asked the Finance Committee to make would revamp the tax reductions for individuals to shift more of the cuts to persons earning $20,000 and under, and less to those with incomes of $50,000 and above.

Blumenthal also asked for a major rewriting of the House provisions affecting capital gains taxes - both to prevent high-income persons from escaping taxes, and to eliminate proposed "inflation adjustment" for capital gains.

Capital gains are the profits from the sale of stocks or other property. Under present law, only half of a capital gain is subject to the regular income tax. The rest may be subject to a 15 percent "minimum tax" designed as a kind of fall back.

Blumenthal also asked the committee to trim a House-passed provision that would give homeowners a once-a-lifetime chance to take up to $100,000 in profits from the sale of their homes tax-free, even if they don't buy a new home.

The administration's new proposal would cut this exemption to the first $50,000 of the profits from a home sale, and limit the tax break to persons aged 55 or over. The purpose of the House bill is to aid retirees.

Blumenthal's appearance marked a more conciliatory posture on the part of the administration, which has suffered a series of major political setbacks on the tax plan, in part because of its reluctance to compromise.

In return, Sen. Russell B. Long D-La), the Finance Committee's chairman, and other panel members seemed generally sympathetic to the administration's proposals. Only the Republicans demurred, supporting a GOP tax-cut plan.

Blumenthal and Long also agreed to "work together" on a proposal to revive a 1963 Kennedy administration plan for cutting capital gains taxes. This would be achieved by exempting more from taxation, rather than by cutting rates.

Long also suggested the panel might consider changing the present system of itemized deductions. Long wants to put a floor under key deductions by denying those below a certain level. He then would allow some itemizing by taxpayer who claim the standard deducation.

The changes Blumenthal said the administration was seeking in the House-passed bill include:

Changing the tax cuts for individuals by scrapping the House-passed increase in the $750 personal exemption and reinstating Carter's proposal to replace it with a $240 credit, which would benefit poorer taxpayers.

Scuttling the House-passed capital gains tax-cut provisions and replacing them with a last-minute administration plan to trim the maximum capital gains tax rate to 35 percent, from the present 49.1 percent now paid by a handful of high-income investors, but would repeal most of the minimum tax and replace it with a weaker levy.

Abandoning the House-passed graduated income tax for small businesses. The administration contends this tax would benefit high-income family-held stores and factories. The present law affecting small businesses would be restored.

Adding to the handful of tax "reforms" the House has approved, by repealing present deductions for business use of yachts and hunting lodges, and tightening House-passed provisions cracking down on abuses of tax shelters.

Blumenthal also asked the Senate to consider streamlining the present "domestic international sales corporation" tax subsidy for exporters to skew the benefits toward smaller firms. Carter earlier had sought to repeal DISC entirely.

In his news conference yesterday, Carter also reiterated his opposition to the tuition tax credit bill both houses of Congress have enacted. But he stopped short of saying flatly he would veto the bill.