Senate Finance Committee Chairman Bob Packwood (R-Ore.) said yesterday he had obtained President Reagan's support for his tax-revision proposal, which would lower tax rates and cut back more sharply on several individual income-tax deductions than the measure passed last year by the House.

Presidential endorsement is considered crucial to moving tax overhaul through a contentious Finance Committee, which is scheduled to begin its drafting sessions next week. Packwood, who presented his proposal to Reagan at a White House session yesterday and to several of his committee colleagues at separate sessions, has structured his plan partly to meet administration objections to the House legislation.

"By and large, they like the bill as we have drafted it and will support it when we introduce it next week . . . . They'll lobby for it," Packwood said of the administration. Administration officials concurred in that assessment. Packwood said Reagan told him, "Bob, from what I know of the outline, I like the bill and congratulate you on a good job in producing it."

Packwood said the package does not include higher taxes to meet congressional deficit-cutting targets; instead, it would bring in the same amount of revenue as the current tax code. Packwood did not rule out adding new revenue later, but he said he did not want "to get it mixed up with a tax increase," at least until new revenue is specifically requested by the Senate Budget Committee.

Packwood met with seven members of his committee yesterday to solicit their support for using his plan as a starting point for overhauling the tax code. He predicted after the meetings that he would get 12 to 13 votes for his plan, saying, "The bulk of those I met are satisfied with the bulk of what's in the draft." He will finish the meetings today and said he will make his tax plan public on Thursday.

But objections began cropping up almost immediately to portions of the document. Sen. Daniel Patrick Moynihan (D-N.Y.) told reporters that the proposed limitation on the deductions for state and local sales, personal-property and income taxes went against "a matter of principle."

New York Gov. Mario M. Cuomo (D), an outspoken opponent of Reagan's earlier proposal to end the deduction for all state and local taxes, said the measure would put "enormous pressure on localities to raise property taxes," which would remain fully deductible.

The Packwood proposals would limit the deduction for state income taxes for taxpayers with incomes of more than $75,000 a year. Instead of deducting those taxes from the top bracket of 35 percent, the taxpayer could only take it against the next-lowest bracket of 25 percent, even if the taxpayer was in the 35 percent bracket.

That change, plus elimination of the deduction for state and local sales and personal-property taxes, would raise revenue by about $27 billion over five years. Repeal of the entire deduction, as Reagan proposed, would have raised about $122 billion.

Sources said one controversial element, a limitation on the deduction companies take for advertising expenditures, had been removed from the plan after it was sent to the Treasury Department for examination last week.

Limitations on deductions for interest on consumer purchases would be considerably tougher than those in the House measure, sources said. The House bill would limit the deduction for interest paid to the sum of interest on mortgages for two houses, plus an amount equal to the taxpayer's investment income, plus $20,000. Under the Packwood plan, the $20,000 would be $2,000.

As previously reported, the Packwood proposal would cut the top individual and corporate tax rates to 35 percent (under the House bill they are 38 percent and 35 percent respectively, and currently are 50 percent and 46 percent), repeal some business tax breaks but give companies more generous investment writeoffs than the House and grant an increase in the personal exemption to $2,000 for taxpayers with incomes below $100,000.

Those making between $100,000 and $200,000 would be given only a partial increase in the personal exemption, which can be taken by all taxpayers and dependents. Taxpayers with incomes above $200,000 would get no increase above the current $1,080 exemption. One source who had seen the package said it was not clear whether the plan would permit those upper-income taxpayers to take any personal exemption at all.

The proposal also includes a 20 percent minimum tax for individuals and corporations, five points lower than the House.