Vice President Dick Cheney, delving into internal Iraqi politics, pushed a Kurdish leader on Tuesday to play a helpful role in passing legislation to foster national reconciliation and forge a new agreement for U.S.-Iraq relations in years to come.

After a rally with troops, Cheney flew to Irbil in the Kurdish region of northern Iraq for a meeting with Massoud Barzani, head of the regional administration in the semiautonomous 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 crucial pieces of national legislation in the days ahead," Cheney said.

Barzani called Cheney's visit a "historic day" in Iraqi Kurdistan.

"We understand very well the importance of this visit," Barzani said. "Indeed, I would like to reinstate 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

"I would like also, Mr. Vice President, to assure you that we are committed to the constitution of Iraq and we will continue to be playing a positive role to be part of the solution, not part of the problem."

It was Cheney's first visit to the Kurdish region. "It's a visit that's long overdue," Cheney said.

He said he and Barzani talked about the overall situation in Iraq as well as what is happening specifically in the Kurdish region. But Cheney did not specifically mention the problems with the Kurdistan Workers' Party, or PKK.

The PKK wants autonomy for the predominantly Kurdish southeastern Turkey, and rebels have carried out attacks in Turkey from bases in Kurdish Iraq. The conflict started in 1984 and has killed up to 40,000 people. The United States has been sharing timely intelligence with Turkey, which recently launched an eight-day ground incursion to attack the rebels.

Cheney focused his remarks on a U.S.-Iraq agreement being negotiated to define the relationship between the two nations in years to come, efforts in Iraq to reconcile the political power among Shiites, Sunnis and Kurds and the need to pass legislation that will lead to a unified government.

Rallying troops after an overnight stay at an air base, Cheney said earlier Tuesday that as long as freedom is suppressed in the Mideast, the region will remain a place of "stagnation, resentment and violence ready for export."

"You and I know what it means to be free," Cheney told the troops at an outdoor rally at Balad Air Base.

"We wouldn't give such freedoms away and neither would the people of Iraq or Afghanistan, but in both of those countries, they're facing attack from violent extremists who want to end all democratic progress and pull them once again in the direction of tyranny.

"We're helping them fight back because it's the right thing to do and because it's important to our own long-term security," Cheney said. "As President Bush has said, the war on terror is an ideological struggle and as long as this part of the world remains a place where freedom does not flourish, it will remain a place of stagnation, resentment and violence ready for export."

After the rally, Cheney, the highest ranking U.S. official to overnight in Iraq, flew to Irbil for his meeting with Barzani.

Later in the day, Cheney was flying to Oman, the next stop on a 10-day trip to the Mideast, which also will include visits to Saudi Arabia, Israel, the Palestinian territory and Turkey.

Cheney and his wife, Lynne, slept in a trailer set up for VIPs at the air base about 40 miles northwest of Baghdad, then had breakfast with some of the 20,000 U.S. troops on the base, which supplies food, fuel, bullets and other items — from toilet paper to military hardware — to all operations in Iraq. It was Cheney's second overnight in Iraq. He spent a night last May at Camp Speicher, a base near former leader Saddam Hussein's hometown and about 100 miles north of Baghdad.

Noise from mortar and artillery shells fired from the base interrupted sleep during the pre-dawn hours Monday, but base officials said later the shelling was routine — used to keep pressure on ground miles off base where insurgents have been active before.

Cheney said he was already up when he heard the explosions. "Nobody came running in to wake me up," he said as he loaded his plate with sausage, bacon and eggs, and hash browns. He and his wife and daughter, Liz, who also spent the night at the base, had breakfast with a dozen or more troops, and Cheney presented two bronze stars awarded for valor.

Hundreds of troops greeted Cheney at the rally where he reaffirmed America's commitment to Iraq and credited recent reductions in violence to Bush's decision last year to send 30,000 more troops to the fight.

"We made a surge in operations and the results are now clear: more effective raids to root out enemies, better and more accurate intelligence information from the locals and higher hopes for the future among the Iraqi people," Cheney said.

The vice president expressed hope that anti-American sentiment generated by the U.S.-led invasion five years ago this week, was waning — at least in Iraq where the U.S. death toll is nearing 4,000.

"Across this country, the more that Iraqis have gotten to know the Americans — the nature of our intentions and the character of our soldiers — the better they have felt about the United States of America," he said.