KABUL, Afghanistan — Afghanistan’s parliament opened yesterday after more than three decades, with President Hamid Karzai making an impassioned plea for the revived body to cooperate in fighting the country’s most intractable problems, including terrorism, poverty and drugs.

As Vice President Dick Cheney looked on from the front row of the reconstructed parliament building, Karzai declared that Afghanistan had achieved its goal of true democracy just four years after the fall of the Taliban. ”With the establishment of the National Assembly, Afghanistan is now a complete country,” he said.

But he also acknowledged that Afghanistan is still a long way from where it needs to be in certain crucial areas. He called on parliament members to work with his government in rooting out corruption, creating jobs, and restoring security following a quarter-century of conflict. ”Without unity, we cannot solve these kinds of problems,” he said.

Cheney did not speak at the ceremony, but he later addressed troops at a rally at Bagram Air Base, a day after meeting with soldiers during a surprise visit to Iraq.

”The victory of freedom in Afghanistan as well as Iraq will be an inspiration to democratic reformers in other lands,” Cheney said.

The seating of the parliament caps the democratization process worked out by international officials and anti-Taliban Afghans in Bonn, Germany, in December 2001. Under that agreement, Afghans created a new constitution in January 2004, and Karzai was elected president that October. The 249 members of the parliament’s lower house, or Wolesi Jirga, were elected this year on Sept. 18. The 102 members of the upper house, or Meshrano Jirga, were later appointed by Karzai or by elected local councils.