Stock prices finally succumbed to weeks of bad international news today as the stock market fell almost continuously from the opening to the closing bell.

The Dow Jones Industrial Average closed at 807, down 14.12 points from Monday.It had been down as much as 15.33 points, at the 3 p.m. reading, but picked up slightly in the last hour of trading.

Market analysts said the sharp decline was the cumulative result of a recent spate of bad news, including the war between China and North Vietnam, continued turmoil in Iran and the round of price increases announced by most oil-producing countries.

But "the straw that broke the camel's back, so to speak," according to E. F. Hutton's Newton D. Zinder, was the decision by Israeli Prime Minister Menachem Begin and his cabinet to refuse President Carter's invitation to come to Camp David to continue Mideast peace talks with Egyptian Prime Minister Mustafa Khalil.

Shortly after the major stock exchanges closed at 4 p.m., President Carter announced that, at his invitation, Begin will fly to the United States Thursday to confer with Carter on the Mideast situation.

But analysts said the move would have little impact on stock prices Wednesday. "Carter's going to try to browbeat him (Begin) into more concessions, but it won't work," one broker said.

Stock prices declined across the board, with only 180 issues posting gains while 1,404 stocks declined. The 14.12-point decline in the Dow Jones average of 30 industrial stocks was the biggest since Dec. 18.

The American Stock Exchange Index closed at 160.51, off 2.85 points from Monday. More than 500 Amexissues declined, while 126 closed higher. Among declining Amex stocks was Resorts International Inc., off 1 7/8 at 46.

Resorts had climbed 4 3/4 Monday and was the most active stock on the Amex after the New Jersey Casino Control Commission granted the company a permanent license to operate a gambling casino in Atlantic City.

There were 31.7 million shares traded on the New York Stock Exchange today compared with 22.6 million on Monday.

The New York Stock Exchange index of common stocks closed at 53.88, down 0.9 point from Monday.

The over-the-counter market mirrored activity in the organized exchanges. The National Association of Securities Dealers reported that 1,054 issues declined while only 139 rose. The most active over-the-counter stock was De Beers Mining, which closed at 6 17/32, up 5/32s from Monday.