Accompanied by some Cabinet ministers and lawmakers, Karzai arrived in Lashkargah, the capital of Southern Helmand province, in the afternoon, Pajhwok Afghan News reported.
Karzai warned if the jail was not completely handed over by the US, the Afghans would themselves think over a strategy, but he did not explain.
Later, speaking at a press conference, Karzai said the Taliban were in service of the US. He said some disgruntled Taliban leaders were willing to hold talks with his administration, but there were other Taliban who traveled in planes with foreigners and his government opposition political forces for talks overseas.
He said there were some Taliban fighters who used foreign guns against their own people, asking such elements to reform themselves and stop promoting the interest of others at the expense of their brothers' lives.
The president also said the full handover of the Bagram jail would take place next week.
The US military two days ago delayed the transfer. The White House said on Monday the US continued to work with Afghanistan on the transfer of the Bagram jail to the Afghans.
In his previous remarks, Karzai said the US doesn't want to leave the country after the NATO's mandate expires at the end of 2014 because it covets Afghan resources and is talking with Taliban leaders behind his back.
"Taliban are every day in talks with America, but in Kabul and Khost they set off bombs to show strength to America,". Karzai said. "The bombs that went off in Kabul and Khost yesterday were not a show of power to America, but were in service to America…It was in the service of foreigners not withdrawing from Afghanistan."