The government will need to borrow about $19.5 billion to cover its bills during the first three months of the year, Under Secretary of the Treasury Anthony M. Solomon said yesterday.

He said the Treasury would raise $1.7 billion of that next week as part of its regular quarterly refinancing of Treasury debt.

Solomon said that during the first half of the year the government is expected to run a cash deficit of $18 billion. "This involves a $27.5 billion cash deficit in the first quarter, about the same as in the first quarter a year ago."

During the second three months of the year, the government will collect about $9.5 billion more in revenues than its expects to pay out, a cash surplus that is a little bigger than the one the government had during the second quarter of 1977, Solomon told reporters.

The Treasury will not need to borrow the full $27.5 billion from the public to cover its first quarter cash shortage.

Solomon said that the government will draw on some of its cash in the till and sell special, non-marketable securities to foreign and local governments. It will have to borrow $19.5 billion from the public during the second quarter.

It will use $5 billion of its $9.5 billion second quarter surplus to pay off outstanding debt and presumably add back to its cash balances the remaining $4.5 billion.

Solomon said that when the borrowings announced yesterday are completed next Thursday, the Treasury will have raised $5.75 billion of the $19.5 billion it will need to borrow before March 31.

The remaining $13.75 billion can be raised using "routine" financing tools such as two-year and four-year notes, cash management bills and additions to the regular weekly bill auctions, Solomon said.

Next week the Treasury will auction $6.75 billion in securities to pay off slightly more than $5 billion of debt issues that are maturing and to raise $1.7 billion in new cash.

The securities include:

$2.5 billion in three-year, three-month notes, to be auctioned Jan. 1. The minimum denomination is $5,000.

$3 billion in seven-year notes which carry an interest coupon of 8 per cent. The notes, which will be auctioned Feb. 1, can be purchased in minimum denominations of $1,000.

$1.25 billion of 27-year, three-months bonds carrying an interest coupon of 8.25 per cent. The bonds can be bought in minimum denominations of $1,000 and will be auctioned Feb. 2.