Former prime minister Yulia Tymoshenko, the charismatic heroine of last year's protests, meanwhile, kept the country guessing about whether she would now move into opposition against her former comrade.
Yushchenko dismissed Tymoshenko's government on Thursday, tossing out of office one of the key drivers behind the protests that swept him to power.
He also accepted the resignation of one of the movement's top financial backers, Petro Poroshenko, a Tymoshenko rival.
"No one wants conflict or misunderstandings," Yushchenko told parliamentary leaders in a closed-door, according to his office on Friday.
"If it appears, I'm convinced it must be met with honesty and courage, and given an absolutely balanced and calm answer."
It is unclear if Timoshenko will
now oppose Yushchenko
The government's break-up, amid allegations of corruption, deepens a crisis that has cut into the popularity of Yushchenko and left him looking isolated, especially in contrast to the broad coalition that joined in last year's mass protests, which many Ukrainians saw as a new start for their nation.
"Independence Square betrayed," declared the daily newspaper, Kievskiye Vedomosti, while the newspaper Den pronounced: "Burying the Revolution."
Tymoshenko so far has been reticent, but some of her allies have called Yushchenko's move a betrayal of his revolutionary comrade, who did more than any of his other allies to persuade protesters to come out the street last year - and then stay until the opposition triumphed.
Radio call-in shows on Friday morning were bursting with support for Tymoshenko.
The sacking of the government
has hit Yushchenko's popularity
"Yushchenko the president is Tymoshenko's creature. He betrayed her, and, thus, showed himself as a shortsighted politician," said Irina Shvets, a doctor.
"Why sack the whole cabinet if the conflict is between Tymoshenko and Poroshenko only? And how could (Yushchenko) put on the same level the real leader and a businessman who lost all sense of proportion?"
Relations between Yushchenko and Tymoshenko, however, had long ago turned tetchy, with Yushchenko repeatedly scolding Tymoshenko for interfering too much in the free market system.
The latest criticism came just last month when the president blamed the government for its handling of the re-nationalisation of one of the world's biggest Ferroalloy plants, Nikopol, suggesting his cabinet had become embroiled in a dispute between two financial groups and giving the appearance that it was handing control from one business group to another.
"Why sack the whole cabinet if the conflict is between Tymoshenko and Poroshenko only?
Radio talk show participant
Tymoshenko insisted that she had done nothing wrong.
If she decides to move into the opposition, she will become a strong challenger to the president, particularly before March parliamentary elections.
"I can predict that our team, which will be headed by Yulia Tymoshenko, will win the parliamentary election and return to its position in April," former vice-prime minister Mykola Tomenko was quoted as telling the Interfax-Ukraine news agency.
Tomenko's resignation and his allegations of corruption against chief of the Security and Defense Council Poroshenko - the second such attack - triggered the government's dismissal on Thursday.
"New appointments should come pretty soon, the pause should not be too long. Otherwise, (Yushchenko) will again face criticism," said Oleksandr Lytvynenko, a political analyst with Kiev's Razumkov thinktank.