BAGHDAD (CNN) -- House Democratic leaders on a visit to Iraq came away convinced that a political solution is necessary, according to a statement released by the office of House Speaker Nancy Pelosi.

Pelosi made the trip with Democratic Reps. John Murtha of Pennsylvania, Ike Skelton of Missouri, Tom Lantos of California, Silvestre Reyes of Texas and Nita Lowey of New York, plus a lone Republican, Rep. Dave Hobson of Ohio.

"We are convinced that there must be a political solution to the problems in Iraq," the statement said. "The sooner Iraqi leaders make necessary political accommodations, including amending their constitution to resolve outstanding differences among all Iraqi communities, the better the chances for ending the sectarian violence. We encourage active diplomacy in the region.

Pelosi and the others, who include the chairmen of several committees, met with Iraqi Prime Minister Nuri al-Maliki, along with U.S. Ambassador Zalmay Khalizad, and senior U.S. military officers, including multi-national commander Gen. George Casey.

"We stressed our belief that it is well past time for the Iraqis to take primary responsibility for the security of their nation," the statement said.

"The delegation's view is that American forces should quickly begin to transition from a combat role to one focused on training, counter-terrorism, force protection, and controlling Iraq's borders."

In the meeting with Maliki, the prime minister emphasized his government's plan to confront terrorists politically as well as militarily, according to a statement issued by al-Maliki's office.

"The PM added that the Baghdad security plan aimed at securing the capital will target all outlaws no matter what their sectarian or ethnic affiliation is," the statement said.