The activists say Karimov has no legal right to run the country until the next election, scheduled for the end of this year.
Karimov was first elected president of independent Uzbekistan in 1991.
His second, five-year term began on January 22, 2000, and was extended for another two years through a national referendum in 2002.
Shahida Yaqub of the London-based Uzbek Initiative nongovernmental group tells RFE/RL that Karimov has no right to seek a third term.
"From January 22 until December 23, when allegedly elections in Uzbekistan are announced, his government and [Karimov] himself are going to be totally illegitimate and therefore everything, every decree, [every] law issued by the government and the president [will be] illegitimate as well," Yaqub added.
Uzbek officials, however, hold a different view.
Constitutional Court Deputy Chairman Bahtiyor Mirboboev told RFE/RL today that the lower house of parliament voted that Karimov should remain in office until new elections are held.
Meanwhile, at least two people have announced their intention to run in the upcoming polls.
One is Tashkent-based rights campaigner Jahongir Shosalimov. Shosalimov told the uznews.net independent information website on January 19 he had sent the Constitutional Court a letter challenging Karimov's right to remain in office after January 22. But he said he had received no reply.
(with material from uznews.net and ferghana.ru)