President Carter, in a letter made public here today, described as "reckless allegations" reports in the U.S. press that former West German Chancellor Willy Brandt had a secret financial relationship with the CIA.

Responding to a letter form Brandt, Carter wrote that he too was "deeply disturbed and deplore the reckless allegations concerning you that are appearing in our press.

Charges that Brandt or the Social Democratic Party, which he still heads, had to some point received money from the CIA have surfaced here and in the United States before and have always denied by Brandt.

In an apparent reference to the resurfacing of earlier allegations, Carter wrote that "I can well understand your outrage that this canard continues to reappear."

"Unfortunately, as a government," Carter continued, "we have to resist the temptation to dignify every report of intelligence activities with a comment. I want to express to you my personal regrets for any embarrassment that those press stories may have caused you.

"I wish it were in my power to prevent these groundless accusations about you. It is the price we pay for the system of government we both cherish," Carter said.

Carter said he was "comforted by the fact that your outstanding reputation as a statesman and leader cannot be affected by unsubtantiated rumors."

The reference to Brandt came in American newspaper reports Saturday that listed Brandt's name along with several government leaders in other countries as those deleted by court order from a critical book on the CIA by two former U.S. intelligence officers. Victor Marchetti and John D. Marks.

Brandt wrote to Carter Saturday, calling the reports totally wrong, denying that he had every received money either for himself or his party, and asking Carter to clarify the allegations. He also said he was sorry "to come up with such a bad subject in our first contact."

The Carter letter appeared to be a strong affirmation that Brandt had no personal financial relationship with the CIA. The letter, perhaps inadvertently, makes no mention of the West German Social Democractic Party.

The press reports last week gave no indication of when such alleged financial relationships took place or what they were for.

Some experience officials here believe the allegations stem primarily from the deleted references in the book "The CIA and the Cult of Intelligence," and from a later article supposedly based on the censored reference that appeared in the U.S. magazine. New Republic a few years ago. In addition, the appearance of a CIA official at a Washington reception for Brandt in 1971, when he was still chancellor, supposedly fed the allegations.

Aside from Brandt's repeated denials of getting any money for himself or his party, those defending his side of this issue here point out that intelligence agencies of all the allied powers, not just the CIA, tried to maintain contacts with the Social Democratic Party, especially in the hectic years here after World War II when it was a minority party.

Brandt, who spent the war years in Scandinavia, returned to German after the war, became mayor of West Berlin in 1957 and chancellor in 1969. He resigned in 1974 after an East Germay spy was discovered on his staff.