United Nations ? President Bush said Tuesday that he was “sick and tired” of Iraq’s failure to cooperate with the United Nations on disarmament and warned that “time is running out.’

But in New York, Secretary-General Kofi Annan said he was “optimistic and hopeful” that pressure on Iraqi President Saddam Hussein could lead to disarming Iraq without military intervention, although he conceded that the threat of U.S. military action was instrumental in forcing Iraq to allow inspections to resume.

The disparate positions reflect differences between the Bush administration and the United Nations about how and when to solve the confrontation over Baghdad’s suspected weapons of mass destruction. They also reflect the bad cop-good cop positions assumed by the two leaders most pivotal to the current U.N. effort.

The United States is intent on ratcheting up the pressure more every day that Iraq balks at complying with requests for information on nuclear, chemical and biological weapons or ballistic missiles. The United Nations is counseling more time and patience for weapons inspectors to do their job — a position held by many of its member states, including close U.S. allies.

But the president’s words also reflect the administration’s effort to adjust its public message on Iraq for the second time in two weeks, according to U.S. officials.

Last week, U.S. officials tried repeatedly to lower expectations that American military action would be imminent after weapons inspectors’ first formal report to the Security Council on Jan. 27. It worked so well in pushing back assumptions about a timetable that the administration is now concerned that Hussein may believe that pressure is letting up or that he has a temporary reprieve.

This week, the administration is again trying to impress the Baghdad regime with the dire consequences of not acting.

“So far, I haven’t seen any evidence that he has disarmed. Time is running out on Saddam Hussein. He must disarm. I’m sick and tired of games and deception. That’s my view of the timetable,” Bush told reporters as he began talks with Polish President Aleksander Kwasniewski.

The White House also insisted Tuesday that the burden of proof remains on Baghdad, not Washington, on disarmament.

“The issue is not how long the inspections will last; the issue is whether Saddam Hussein this time is finally willing to disarm,” said White House Press Secretary Ari Fleischer. “The inspectors have more time, but time is running out. This is a question of not allowing Hussein to string the world along forever.”

The State Department charged Tuesday that Iraq was responding to weapons inspections with only superficial cooperation, inadequate disclosures and continued defiance. “In other words, Iraq is not coming clean,” spokesman Richard Boucher said.

Just days before the two top inspectors are due to travel to Baghdad for talks, National Security Adviser Condoleezza Rice met with chief weapons inspector Hans Blix on Tuesday in New York to press for accelerated U.N. interviews with Iraqi scientists and more U.S. intelligence-sharing, according to administration officials.