The unemployment rate dropped from 6 to 5.8 percent last month as the number of jobs in the economy increased by at least 300,000, the Labor Department reported yesterday.

There were 95.2 million people at work, 5.9 million jobless and looking.

President Carter seized on the favorable news, telling a campaign crowd in Portland, Ore., that the higher interest rates and other steps he announced Wednesday to bolster the dollar will not produce the recession some analysts fear.

"Our country is going to stay a strong bulwark against depression throughout the world," the electioneering president said.

In other economic developments:

The dollar gained ground on international money markets for the third straight day since Carter announced his plan to support it Wednesday.

Interest rates continued to rise in response to Federal Reserve Board actions. The prime rate that banks charge their best corporate customers rose from 10.5 to 10.75 percent, its second increase in a week. At the same time, the Federal Home Loan Bank Board reported that home mortgage rates rose to a record 9.84 percent nationwide, up from 9.73 percent in September.

Stock prices raised. The Dev Jones industrial average rose 6.15 points, after falling 10 on Thursday.

Charles L. Schultze, chairman of the president's Council of Economic Advisers, said yesterday that the steady improvement in the nation's employment picture demonstrates that the economy is strong enough to handle the higher interest rates that are believed needed to strengthen the dollar.

Schultze, testifying on the president's new inflation plan before the Senate Banking Committe, said there are risks to raising interest rates but that the risks of a continuing decline in the value of the dollar, which has that effect of raising prices domestically, are "much greater."

Meanwhile, the White House and organized labor continued their shouting match over the president's new wage-price guidelines program.

AFL-CIO President George Meany has called the program inequitable and urged mandatory wage-price curbs instead, a position that was reiterated yesterday before the Senate Banking Committee by AFL-CIO research director Rudolph Oswald.

But Alfred Kahn, the administration's new anti-inflation czar told the same committee it is "ludicrous to hear George Meany talk of the inequities of this program" and call for mandatory curbs. A few years ago, Kahn said, Meany was "talking of the inequities of the mandatory" program in the Nixon administration. Kahn said the new program is fair.

The nation's unemployment rate has been hovering near 6 percent for most of the year. At 5.8 percent, however, the rate is a full percentage point below its October 1977 level. During the same 12 months, the number of employed Americans has grown by 3.6 million.

The unemployment rate is calculated from a survey of 56,000 households. Another survey, taken from employer payrolls, shows that employment grew by 3.4 million during the last year. The payroll survey is less comprehensive than the household survey, but is considered more accurate. It does not cover self-employed persons of farm workers.

The number of persons holding jobs stood at 95.2 million up from 94.9 million in September. About 5.9 million persons were looking for work last month, compared with 6 million in September.

According to the payroll survey, nonagricultural employment grew by 430,000 in October, with nearly all major industry, categories reporting increases in jobholders.

The unemployment rates for nearly all major groups improved, with the exception of adult men, who remained constant at 4 percent, and black workers, whose unemployment rate rose from 11.2 percent to 11.4 percent.

The unemployment rate for adult women fell from 6 percent to 5.6 percent, while the teen-age unemployment rate fell from 16.6 percent to 16.3 percent. The white unemployment rate declined from 5.3 percent to 5.1 percent.

The unemployment rate is the percentage of the labor force that is out of work and actively seeking a job. The labor force is the sum of those who have jobs and those who are looking for them.

There were 101.1 million Americans in the labor force last month.