In a live address to Yushchenko on the Ukraina TV channel on Tuesday, Kravchuk said: "The true patriotism of a president... also means understanding the situation from within and making a responsible decision to step down. Such a step could stop the avalanche of problems, calm society and give hope for a real way out of the crisis."
Kravchuk was elected Ukraine's first president in 1991 with 61.6% of votes.
"Until recently I thought the presidential elections should be held according to law. But today I have a different opinion. I have seen clearly that you are not giving most of your attention to Ukraine's problems, instead you are thinking of how to stay in power," Kravchuk said.
The first president of the ex-Soviet republic also accused Yushchenko of betraying the nation's confidence and support, and destroying both the government and the parliamentary coalition.
"The power has been almost destroyed. And it is impossible to overcome the crisis without the government's effective participation," Kravchuk said, adding that the only way out would be to hold early elections.
Parliament speaker Volodymyr Lytvyn told another TV channel on Tuesday that he did not think that early parliamentary elections would be held in Ukraine and said Kravchuk's comments could "provoke another spiral of political confrontation in Ukraine."
Yushchenko has been at loggerheads with Prime Minister Yulia Tymoshenko for several months as the former allies in the "orange revolution" jostle for position ahead of presidential elections due next year.
The country is struggling amid the global economic crisis and had gas supplies from Russia cut off for much of January after failing to agree a new gas contract. Although a 10-year supply agreement was signed barely a month ago, Ukraine's state-run Naftogaz has already warned Gazprom that there may be problems paying for deliveries due to non-payment by local utility companies.
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