NEW YORK (AP) _ In an effort to calm Japanese outrage over the gang rape of a 12-year-old girl on Okinawa, Defense Secretary William Perry announced Wednesday a series of steps ranging from a ``day of reflection'' to increased security patrols on the island.

Perry outlined the measures at a ceremony signing a new security agreement under which Japan will increase to $5 billion a year its payment toward the cost of stationing 40,000 U.S. troops on its territory.

Japan has been paying $4.8 billion a year, which is about 70 percent of the cost.

After signing the agreement, Secretary of State Warren Christopher said it would make ``a very strong alliance even stronger'' and went on to say he was ``deeply distressed ... over the tragic incident in Okinawa.''

``We sincerely regret that this very unfortunate incident in Okinawa took place,'' said Foreign Minister Yohei Kono, who signed the agreement for Japan.

While voicing appreciation for the steps the United State was taking to improve discipline, Kono also made it clear Japan wanted changes in the way criminal cases involving U.S. troops are handled.

Three U.S. servicemen were arrested by military police and are being held pending possible indictment by Japanese authorities. Only then will they be turned over to the Japanese for trial.

If they had been arrested by the Japanese police, they would have remained in the custody of that country.

The signing took place after a meeting between Christopher and Perry and their Japanese counterparts, the first time all four had met together to discuss U.S.-Japanese security relations.

``When any of our military personnel violates the hospitality of the host country, it is not only an action for which that person must be held individually responsible, but it also reflects on the United States,'' said Perry.

He said that the Marines on Okinawa would suspend normal training for ``a day of reflection'' and that religious services this weekend would focus on that reflection.

In addition, he said senior officers and enlisted personnel would participate in a session on how to increase discipline. He said coordination would be improved between the military and the civilian authorities on Okinawa.

He announced an increase in security patrols and said rules for consumption of alcoholic beverages would be tightened.