Cheney was expected to push for resolution of the country's political woes as he headed to Kurdish areas to meet with Barzani in Abril, The Los Angeles Times reported Wednesday.

"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 advance crucial pieces of national legislation in the months ahead," Cheney said before leaving for Oman.

Meanwhile, members of Tawafiq, the main Sunni Arab parliament coalition, refused to attend a two-day meeting in Baghdad because of complaints about the Shiite-dominated government.

Shiite Muslim cleric Moqtada Sadr's bloc walked out, as did a contingent led by Sheik Ali Hatem Sulaiman, a representative of Sunni Muslim tribes that rose against the insurgent group al-Qaida in Iraq.

"It is the Tawafiq bloc's opinion that current circumstances hinder the success of such conferences," parliament member Iyad Samarrai told the Times.

Saad Muttalibi, a conference organizer, accused the Sunni bloc of trying to discredit Iraqi Prime Minister Nouri al-Maliki.