The government published a batch of fresh statistics yesterday suggesting the economy is rebounding strongly now in the wake of the blahs that occurred earlier this year, during the cold weather spell and the coal strike.

In separate reports, statistics-gathering agencies disclosed that the personal income of Americans rose at a robust 1.2 percent annual rate in March - more than twice February's 0.5 percent pace and the biggest jump since December.

At the same time, officials said housing starts continued at a vigorous 2.074 million annual rate in March - maintaining the pace of previous months. New building permits also held firm, suggesting the surge will go on.

The combination of figures appeared to support predictions by analysts that the economy will stage a strong comeback in the second quarter, following a hiatus in January and February.

Jody Powell, President Carter's press secretary, said the statistics show the economy now is "rebounding rather strongly," and forecast that the basic economic indicators should remain robust for at least two or three more months.

However, Powell asserted there is "absolutely nothing" in the figures that "conflicts" with the administration's support for a massive income-tax reduction, such as the President has proposed in his tax cut and "reform" package.

Powell said that unless the full $24.5 billion tax cut is enacted, there will be "a very serious threat" of an economic slowdown late this year or early in 1979. Carter's tax package is designed in part to avert such a slump.

The rise in personal income spurred the overall figure at a $19.4 billion annual pace to a new rate $1.652.2 trillion . Wages and salaries grew at a $15.8 billion pace in March, compared with $8.8 billion in February.

In February, personal income had risen at a revised $7.6 billion annual rate to a new pace of $1.633 trillion. By contrast, January's rise was at a scant $2.5 billion rate, or an annual pace of only 0.2 percent.

The strong performance of housing starts appeared to represent a decided return to the robust pace of earlier months, following a lull in January resulting from the cold weather bout.

However, Kenneth M. Plant, economicist for the Federal Home Loan Mortgage Corp., predicted that construction activity would decline in the second half of 1978 as home mortgage interest rates increase.

Plant said mortgage rates on prime 30 percent loan-to-value loans already have climbed to 9.33 percent, from 8.9 percent recorded last autumn.Some California mortgage lenders already are posting rates of 9.75 to 10 percent.

The reports came as, separately, the government announced that foreign investors remained as active in the U.S. market in the first half of 1977 as they were in the four preceding years.

Official figures indicated that completed foreign direct investment in the U.S. will be substantially higher in 1977 than in 1976, the government noted. The 1977 figures are the latest that are available.

The performance of key economic statistics is being watched closely these days both by administration policymakers and by Congress. The two are embroiled in a growing debate about implications for government economic policy.

Some lawnmakers appear to be convinced that the recovery is going so well that Congress does not need to enact the president's tax-cut proposals, and instead would do better to reduce the federal budget deficit as an anti-inflation measure.

However, the White House - and most mainstream economists - contend a sizable tax reduction still is needed, if only to avert a "drag" on the economy from the increase in individual tax burdens resulting from inflation.

The government is scheduled to publish its quarterly report on the gross national product today, showing the economy slowed during the winter months.