Kaputikyan was increasingly critical of the government of independent Armenia's second president, Robert Kocharyan. On 14 April 2004, she wrote an open letter titled "Kocharyan Must Go" («Քոչարյանը պետք է հեռանա»), where she called for his resignation and protested the violent crackdown on an opposition demonstration on 12/13 April, which left dozens injured. She also returned the Mesrop Mashtots Medal she had been awarded by Kocharyan in 1999. Regarding the beating of the opposition politician Ashot Manucharyan, Kaputikyan stated: "Beating in Armenia has become the basic means of politics and the most influential part of state terror. All cases when force has been used should be viewed from this standpoint." ArmeniaNow reported that she thus became "an opposition celebrity". She also wrote that a responsible politician would have resigned after the 1999 shooting in the Armenian parliament when Prime Minister Vazgen Sargsyan and Parliament Speaker Karen Demirchyan were assassinated, among others. In response, Kocharyan stated that the Mesrop Mashtots Medal is not his medal, but that of the Republic of Armenia. He added that he regrets that is how Kaputikyan's views the "essence of our state" and does not contribute to "our nation's respect for education of the young generation."