After years of cold-shouldering the United Nations, the United States now sings its praises and increasingly suggests things for it to do. But U.S. dollars to match the tasks are not forthcoming, and the United States remains the biggest U.N. debtor.

The United States is urging the world body to take on more responsibilities - from monitoring the Soviet withdrawal from Afghanistan and Cuban withdrawal from Angola to fighting terrorism and drug trafficking and investigating human rights abuses and chemical warfare.It also is expected to monitor the eventual Vietnamese withdrawal from Cambodia and to play a role in a Middle East settlement.

But little money is forthcoming from the U.S. Congress to fund the burgeoning U.S. agenda for the 159-nation organization. The United States is the largest U.N. contributor, assessed one-quarter of the annual budget of $800 million.

While the United Nations has registered a series of formidable peacemaking and peacekeeping successes that advance U.S. interests, Congress has been withholding U.S. dues.

The United States ended 1988 about $402 million in arrears in budget and peacekeeping dues - 53.5 percent of the total U.N. arrears of more than $750 million.

Largely because of U.S. non-payment, the United Nations periodically faces financial crises and is having trouble paying for new peacekeeping operations.

President Bush, a former U.S. ambassador here, praised the United Nations during his election campaign and called for the payment of U.S. dues.

Congress has been withholding a large part of the dues because of budget constraints and disaffection with the world body. The organization was seen as biased against the United States, bureaucratically bloated and wasteful.

Some money was withheld in an effort to force the United Nations to reform itself, despite administration and State Department calls for full-funding.

George P. Shultz said before leaving office as secretary of state said it is important for U.S. foreign policy "to fully fund our contributions to U.N. agencies . . . and to initiate a plan to pay arrearages . . . over a five-year period."

He said the request for nearly full payment of dues "is critical to our objectives of resolving regional conflicts. The U.N. can play an important role in this regard."

U.S. Undersecretary of State Richard S. Williamson, in charge of international organizations, said, "Up through last year, the Executive, State Department and White House sought full funding. Congress failed to appropriate the full amount."

Last year, the United Nations scored spectacular achievements and its peacekeeping forces won the Nobel Peace Prize.

In Afghanistan, U.N. observers are monitoring Soviet withdrawal under a U.N.-mediated agreement. For years, ending Soviet involvement in Afghanistan was a prime U.S. foreign policy goal.

In the Persian Gulf, U.N. peacekeepers are monitoring a cease-fire while Iran and Iraq are talking under U.N. auspices. The cease-fire enabled the United States to scale back its costly naval presence there.