He was commenting on Holy's claims that she had been spied on, for which she would press charges.
Holy resigned on Thursday, a day after the national broadcaster published on its website an e-mail she sent to the head of state railway company HZ, Rene Valcic, in March, asking him to keep the wife of a party colleague in her job.
Josipovic agreed with Holy's statement that the e-mail had been an ill-advised move for which she was paying the political consequences, but said she had launched important reforms and made very good things, so he hoped her successor would keep up her work.
Commenting on the media's fear that other government members were being wiretapped and spied on, Josipovic said one should not spread paranoia.
"What I can certainly tell you, considering my position and powers, is that those whose job it is to monitor those who endanger security and break the law, is that there are no such abuses."
The president said he had a good insight into the work of the secret services because that was his job and that he was not afraid that someone was checking his e-mails.
He went on to say that the dissatisfaction of citizens and the decline in the government's popularity were the result of the crisis and that this was understandable.
"Times are hard. The government has to make many difficult moves and I am confident the government will make them," he said, adding that one must bear in mind that a state, if it was not a welfare state, did not make much sense.
Josipovic said that from the beginning of the year, when it stepped into office, the government had taken some steps, such as the position on the budget and the major investment plans, that could give hope that things would get better.
He added, however, the regulations halting investors, as well as making life difficult for citizens, had not been completely "loosened up."
Josipovic reiterated that he would not attend Monday's inauguration of Serbian President Tomislav Nikolic in Belgrade, saying he expected Nikolic to make the first move, as he had to show that now he thought differently than in the past.
Josipovic said Nikolic's statements after his election were not conducive to good cooperation, but that one should be pragmatic and wait to see what Nikolic would do in his term.
As for the gay pride parade held in Split on Saturday, Josipovic said Split and Croatia had passed the test, as the event was peaceful, without violence and in the spirit of tolerance. He added that the strong police force showed that the state was ready to prevent any possible riot and that it had learned from last year's experience, when Split Pride was marred by violence.