(Adds quotes) By Claudia Parsons BAGHDAD, Nov 2 (Reuters) - The U.S. military said on Thursday it believed an American soldier who was abducted in Baghdad 10 days ago is still being held by his captors. U.S. military spokesman Major General William Caldwell also told a news conference there was a "tremendous amount of political activity" under way to secure the release of the U.S. soldier of Iraqi descent, who was kidnapped by gunmen while visiting relatives after leaving the security of the Green Zone. Caldwell identified the soldier as Ahmed al-Taie, a 41-year-old linguist and said he was visiting family "including his Iraqi wife" when he was kidnapped. His family told reporters he was taken by Shi'ite militiamen. "At this point we believe the ones who kidnapped Ahmed currently still have him," Caldwell told reporters. Asked if the U.S. military had been in contact either directly or indirectly with the kidnappers, Caldwell said: "There is ongoing dialogue that is being done at different levels at this time, but it would be inappropriate for me to state with whom or at what level." U.S. troops lifted roadblocks around the Shi'ite slum district of Sadr City on Tuesday when Prime Minister Nuri al-Maliki ordered them out, flexing his political muscle after a week of public friction with Washington ahead of U.S. elections. The checkpoints, part of a massive U.S. effort to find the kidnapped U.S. soldier, had brought gridlock to several parts of the city and drawn the ire of Sadr City residents who complained of collective punishment. Sadr City is a stronghold of the Mehdi Army, a militia loyal to Shi'ite cleric Moqtada al-Sadr, who recently ordered rogue elements of the militia to step back into line. Maliki, who depends on Sadr's movement for key support in parliament, has struggled to crack down on militias blamed by Sunnis and Washington for operating death squads. Caldwell said U.S. military operations were still underway in Baghdad to find the soldier, focused on the area east of the Tigris river between Sadr City and the mixed area of Karrada. "We do have credible intelligence that indicates who might be associated with this kidnapping and we are vigorously pursuing every lead," Caldwell said. Asked about U.S. policy towards Sadr, whose supporters rose up against U.S. forces on two occasions in 2004, Caldwell said: "He's a part of this political process. From the comments he's made recently he wants to see violence reduced. He wants to see greater peace and security for Iraqis." Caldwell said Maliki's government was "actively supporting" the search for the missing soldier, a reservist deployed to Iraq in November 2005. He said Taie got married in February 2005. "He was married to his wife before he deployed over here," he said. "At the time he was abducted his wife was in (the) country." Caldwell said 32 suspects had been detained during the search and one U.S. soldier killed and eight wounded.