IRBIL, Iraq — Vice President Dick Cheney played the part of backroom power broker for two days and came away on Tuesday with pledges from Shiites, Sunnis and Kurds to firm up a new blueprint for U.S.-Iraq relations that will stretch beyond the Bush presidency.

Cheney flew in a cargo plane to Iraqi Kurdistan in the north to finish two days of private meetings with powerful politicians in Iraq. On Monday, he had talks with officials in Baghdad _ even venturing outside the secured Green Zone to dine and have private discussions.

Topics ranged from security in Iraq to Iran's rising influence in Mideast, but a key item was about crafting a long-term agreement between the U.S. and Iraq, plus a narrower deal to define the legal basis for continued U.S. troop presence.

The deal would take the place of a U.N. Security Council resolution that expires in December, the same time Bush will be packing up to leave office. The administration says the deal will not seek permanent U.S. bases in Iraq or codify troop levels, nor tie the hands of a future commander in chief as some Democrats fear

Administration officials say they probably will not seek Senate approval of the plan because the agreement will not be a treaty that provides Iraq with specific security guarantees. This position has prompted a backlash in Congress, where Democrats have proposed legislation that would render the agreement null and void without the Senate's blessing.

Democrats and some Republicans have questioned whether the 2002 authorization of force in Iraq still applies legally because it referred to the need to get rid of Saddam Hussein and eliminate the threat of weapons of mass destruction. Since the 2003 invasion, Hussein has been captured and executed, and no weapons of mass destruction were ever found.

Cheney advisers said that President Jalal Talabani, a Kurd, made clear on Monday that even though the Kurds have a seniautonomous region in northern Iraq, they were completely committed to making the area work within an Iraqi state.

Cheney was warmly greeted in Irbil by Massoud Barzani, head of the regional administration in the semiautonomous Kurdish area. "We are certainly counting on President Barzani's leadership to help us conclude a new strategic relationship between the United States and Iraq, as well as to pass crucial pieces of national legislation in the months ahead," Cheney said.

Barzani said the Kurds are committed to being "part of the solution, and not part of the problem."

"I would like to reiterate our commitment that we will continue to play a positive role in order to build a new Iraq _ an Iraq with a foundation of a great federal, democratic, pluralistic, free Iraq," Barzani said.

Cheney spent Monday night at Balad Air Base, northwest of Baghdad. On Tuesday morning, before he headed to northern Iraq, he spoke at an outdoor troop rally, saying that as long as freedom is suppressed in the Mideast, the region will remain a place of "stagnation, resentment and violence ready for export."

Later in the day, Cheney flew to Oman, continuing his 10-day trip to the Mideast, which will include visits to Saudi Arabia, Israel, the Palestinian territory and Turkey.