With the United Nations exercising legal authority in Kosovo and long-delayed confirmation hearings for U.S. ambassador-designate Richard C. Holbrooke scheduled to begin this week, a new drive is underway to persuade Congress to pay this country's debt to the world organization.

Former Republican national chairman Haley Barbour is the lobbying point man. His client is the Better World Campaign, a small Washington organization established with money from media tycoon Ted Turner to promote the United Nations.

Barbour's mission is to persuade Congress to enact legislation authorizing release of funds already appropriated without attaching an antiabortion rider that induced President Clinton to veto a similar bill last year. Barbour declined to discuss his strategy, as did Rep. Christopher H. Smith (R-N.J.), sponsor of the rider, who has indicated his determination to attach the veto-bait language once again.

The Better World Campaign has enlisted the support of the U.S. Chamber of Commerce, an influential business group, which last week invited U.N. Secretary General Kofi Annan to make a pitch to members at a Washington dinner.

"The United States has now been in arrears in its payments to the United Nations for 13 years," Annan said. "The private sector, more than any other, understands the meaning of a contract. It is a matter of honor, of keeping one's word. Failing to live up to such obligations has cost the United States dearly, diminishing its stature."

Annan promoted the United Nations as "business friendly" and the stabilizing force that makes international commerce possible.

According to U.N. figures, the United States owes about $1.5 billion. If the debt is not substantially reduced by year's end, the United States will lose its vote in the U.N. General Assembly, joining such deadbeats as Equatorial Guinea, Kyrgyzstan and Yugoslavia.

More than half the debt is for peacekeeping activities that the United States voted in favor of undertaking, which means it is owed not to the world body itself but to the armed forces of friendly nations that went to such trouble spots as Bosnia at U.S. behest. The United States disputes some of the arrears, but acknowledges owing slightly more than $1 billion.

The Clinton administration has been wrestling with the debt problem for years. It was the main reason Secretary of State Madeleine K. Albright, as U.N. ambassador in Clinton's first term, engineered the departure of former U.N. Secretary General Boutros Boutros-Ghali, who was so unpopular with Congress that the Albright feared the money would never be appropriated.

Congress has been sympathetic, to a point. Two years ago, Congress appropriated $819 million, to be paid over three years on condition that the United Nations cut its budget and undertake administrative reforms. With $107 million in U.N. debt to the United States that would be written off, the package totaled $926 million.

But the money has never been spent because legislation authorizing release of the funds came with a condition attached by Smith that the White House refused to accept: restrictions on the use of U.S. funds to aid family planning organizations overseas that work to ease restrictions on abortion. Even though the restrictions were watered down to win Clinton's acceptance, he vetoed the bill.

For much of this year, the administration has said little about the U.N. issue. One reason is that the administration bypassed the Security Council in organizing NATO's air war against Yugoslavia, fearing a Russian veto of any military action. It was difficult to make the case that the United Nations is essential to world peace while cutting it out of a world crisis. Now an agreement with Russia has produced a Security Council resolution authorizing a peacekeeping mission in Kosovo, returning the United Nations to the center of the action.

Another reason for reticence, administration officials said, is that the legislation authorizing release of the funds carries with it requirements that the United Nations reduce the share of its budget charged to the United States. Without an ambassador, the administration did not believe it could persuade other members to accept Washington's terms.

Holbrooke, a renowned persuader and arm-twister, will be expected to take on that assignment, assuming he is confirmed.

Still, to the distress of some U.N. supporters, the administration has not tried to force the issue in Congress.

"I'm not going to tell you our strategy, if we have one," a senior administration official said.

The 1997 Balanced Budget Act set aside $1 billion for U.N. payments outside the spending "caps" that restrict other spending. It is "no year money," meaning it can be spent whenever authorizing legislation is enacted and the United Nations meets the reform requirements demanded by Congress.

But unless the money is spent by Sept. 30, 2000, the end of fiscal 2000, the exemption from the spending caps will expire. In that case, the U.N. debt would have to compete with other budgetary items, making it vulnerable to being raided for other purposes.

"Legislation takes time. If it's not done in the context of the fiscal 2000 budget, it's problematic next year, an election year," said Craig Johnstone, a former State Department budget official now at the U.S. Chamber of Commerce.

The Senate Foreign Relations Committee has approved a State Department authorization bill that would release the funds. The House bill, drafted in Smith's subcommittee, contains no U.N. funding language -- and no antiabortion rider. If the Senate language is retained by a House-Senate conference, Smith could try to persuade conferees to attach the rider. According to lobbyists and congressional staff members, House leaders have said they will not seek to prevent Smith from doing so.