Boeing Co.'s third-quarter and nine-month earnings rose from year-earlier levels, but sales fell in both periods, the aircraft manufacturer reported yesterday.

Meanwhile, National Intergroup Inc. said that sagging income in financial services and steel reduced its third-quarter profits from year-earlier levels.

Another major steel concern, Armco Inc., said it lost $272.7 million in the third quarter, although the deficit was narrower than the $421.5 million loss recorded by the company a year earlier.

Boeing Co. Chairman T. A. Wilson noted that his company had to restate its 1984 first-quarter earnings because the Tax Reform Act of 1984 permanently exempts from federal income tax previously deferred earnings from Boeing's domestic international sales corporation.

Boeing officials attributed increased pretax earnings primarily to continued favorable performance on U.S. government programs and increased interest income. But they added that those increases were offset by lower jet transport sales volume, an "extremely competitive" market and the rising cost of high-level research, development and engineering programs.

Third-quarter earnings were $86 million (88 cents a share) on $2.1 billion in sales, compared with 1983 third-quarter earnings of $75 million (78 cents) and sales of $2.2 billion.

Earnings for the first nine months of 1984 were $266 million ($2.74), compared with $257 million ($2.66) a year earlier, and sales were $7 billion, down from $8.3 billion.

After the restatement of first-quarter earnings, which allows an adjustment to the federal income tax provision of $397 million ($4.08), earnings for the nine-month period were $663 million ($6.82).

In the latest quarter, Boeing received orders for 55 jets, valued at approximately $2.4 billion, compared with orders for 72, valued at $2.8 billion, during the same period of 1983.

National Intergroup Inc.'s third-quarter profits fell to $7.6 million (18 cents a share) from $18.2 million (80 cents) in the 1983 third quarter, the company said yesterday.

The main drags on profits were NII's First Nationwide Financial Corp. and National Steel Corp., the sixth-largest U.S. steel producer, Chairman Howard M. Love said.

"Higher interest rates reduced First Nationwide's net interest margins, while volume and price weaknesses in the markets served by our metals businesses affected National Steel's profitability," according to a statement issued by Love.

"While we expect these adverse conditions to persist in the short term, earnings should be in the black for the final three months and solidly in the black for the year," he said.

Third-quarter sales totaled $548.4 million, including $292 million in cash and notes from Nippon Kokan K. K. of Japan for 50 percent of National Steel.

The steel company earned $11.1 million in the third quarter. NII's equity income from its share of the company totaled $3.5 million in September.

Third-quarter equity income from NII's 83 percent interest in First Nationwide Financial declined to $3.9 million from $7.3 million in 1983.

NII posted nine-month profits of $39.8 million ($1.39) on sales of $2.1 billion. In the 1983 period, NII lost $116.4 million ($6.27), including a write-off of $100 million on the sale of its Weirton Steel division.

Meanwhile, third-quarter operating profits from NII's wholly owned National Aluminum Corp. subsidiary rose to $11.1 million from $8.6 million. Distribution group companies reported a decline in net income to $1.4 million from $2.7 million, and profits in NII's diversified group companies fell from $4.9 million to $279,000.

Armco Inc. said that its third-quarter net loss included a pretax operating loss of $22.7 million and $205 million of special charges against income, primarily related to the company's oil field-equipment business.

The charges include an estimated loss for liquidation of excess inventories in the oil field-equipment unit, and for the consolidation of operations in Armco's bid to utilize better the division's plant and equipment.

Armco said "an excess supply of oil and natural gas in world markets continues to depress demand for oil field-drilling equipment."

The third-quarter loss also included the reversal of an $80.8 million tax credit.

A year earlier, the company's pretax loss from ongoing lines was $48 million, its loss from discontinued operations was $75.4 million and special charges against income -- primarily related to the shutdown of its Houston steel mill -- totaled $296.7 million.

Third-quarter revenue edged up to $1.15 billion from $1.04 billion.

In its specialty steel business, Armco complained that "a surge o imports of stainless flat-rolled steels and electrical steels, added to the normal summer lull, decreased revenues and operating profits."

Armco posted a nine-month loss of $230.5 million on revenue of $3.42 billion, compard with a 1983 nine-mongth loss of $625.7 million on revenue of $3.1 billion.