John W. Hinckley Jr., who is accused of attempting to assassinate President Reagan, says in a letter that his cross-country travels before the March 30 shooting were part of his effort to reach and be near actress Jodie Foster.

In an unsolicited letter to a Washington Post reporter dated Sept. 7, Hinckley wrote, "You and the other journalists make it sound like I was some kind of a hobo or something. My recent cross-country ventures were necessary because New Haven was so far away. I would have traveled to Budapest to find Jodie Foster. Now that I'm in Maryland, she and I are much closer, in more ways than one."

The letter, neatly written in black ink on lined paper, was signed "Yours truly, John Hinckley Jr."

Hinckley is now in federal custody. In the letter he attributes his travels to his deep interest in Foster--an attraction that apparently continues to this day. Asking that he not be called a "drifter" in future news articles about him, he says, "I may have done some drifting in the Fall of 80, but in the years prior to this, I was not roaming around the country."

Foster was in her freshman year at Yale University in New Haven, Conn., at the time the president was shot. Law enforcement officials, who confiscated an unmailed letter to Foster from Hinckley's Washington hotel room and dated the day of the shooting, believe that Hinckley tried to kill the president to impress Foster.

In that unmailed letter to Foster, dated March 30, Hinckley wrote, "Jodie, I'm asking you to please look into your heart and at least give me the chance with this historical deed to gain your respect and love."

Hinckley traveled from Los Angeles to Washington in the months before the shooting, lived for a short time in a cut-rate motel in Denver, and was arrested in Nashville, Tenn., after a security officer found two pistols in Hinckley's luggage.

When Hinckley wrote to Foster, on the date of the shooting, he acknowledged that he had pursued the young actress for months with notes, letters and telephone calls and said he had been hanging around her college dormitory on the Yale campus.

It was not at all clear this week why Hinckley might be annoyed at the way he has been portrayed in news accounts or what he might have meant by the suggestion that he and Foster were now somehow close.

Hinckley's defense lawyer, Vincent J. Fuller, Justice Department officials and the U.S. attorney's office in Washington have refused to discuss the Sept. 7 letter from Hinckley.

In order to independently establish the authenticity of the Sept. 7 letter, The Post sent a letter to Hinckley, using the return address at Fort Meade, where he is being held, which was listed on the original letter and its envelope. Hinckley was also asked to initial a photocopy of the original letter and return it to The Post to help verify its authenticity.

Last Friday, The Post received the photocopy of Hinckley's original letter marked in the lower right-hand corner with the initials "JWH." On the back of the copy was a brief note dated Sept. 14, which said:

"My attorneys are trying to hold the press coverage to a minimum and therefore will have nothing to do with reporters."

The note said, "I am enclosing a portion of a legal paper as proof that I am me. " It was signed "J. Hinckley."

The enclosure appeared to be part of a document filed in the U.S. District Court in Washington in which Hinckley waived his right to appear in person at his bond hearing last Sept. 1. The heading reads in part, "United States of America v. John W. Hinckley, Jr.," and lists the criminal case number assigned by the court. That number was partially crossed out in black ink on the piece of the document sent to The Post.

The first letter received at The Post was postmarked in Prince George's, Md., and the second was postmarked in Washington, D.C. Officials at Fort Meade, in Anne Arundel County, have referred all inquiries about Hinckley to the Justice Department, which has refused to discuss the letters. Officials have said that Hinckley is permitted to receive mail at Fort Meade. Efforts to reach Hinckley by telephone were unsuccessful.

Following his arrest, Hinckley was held at the federal correctional institution at Butner, N.C., where he underwent extensive psychiatric tests to determine if he were competent to stand trial on the charges against him and if he was responsible for his acts at the time he allegedly shot Reagan and three other men outside the Washington Hilton hotel.

The report on the tests has been submitted to the federal court but it is sealed from public disclosure. Hinckley was transferred from Butner to the brig at Quantico Marine Base last Aug. 17 and later moved to Fort Meade.

Hinckley has since pleaded not guilty to all the charges against him.

U.S. District Judge Barrington D. Parker, who will preside at Hinckley's trial, has given his defense lawyers until Sept. 28 to decide if they will argue that Hinckley is not guilty of the charges against him either because he was insane at the time of the shooting or because his mental capacity was so diminished that he should not be held criminally responsible for his acts.