Karimov, the first president of Uzbekistan, died in a hospital following a stroke on September 2 at the age of 78.
"I am here in Tashkent these few days representing the US government so that I can express condolences on the death of President Karimov and also to show our continued commitment to our partnership with Uzbekistan," Rosenblum said during his visit to Uzbekistan.
In Tashkent, Rosenblum met with Uzbek Foreign Minister Abdulaziz Komilov. The US senior diplomat said that he had passed to Komilov a letter by US President Barack Obama, who expressed condolences over Kraimov's death on behalf of the whole US nation.
Rosenblum said that the Uzbek side had also expressed a desire to maintain stability in bilateral relations.