He is expected to begin the consultations on the morning of April 2, and he says if they fail he will dissolve the legislature.
Yushchenko on March 31 reiterated his threat first made two days earlier, accusing lawmakers of failing to respect earlier agreements and abide by the constitution.
Later that day, thousands of pro-Western opposition supporters rallied on Independence Square to urge Yushchenko to follow through on his threats.
Tymoshenko Joins In
Supporters of opposition leader Yuliya Tymoshenko joined the March 31 demonstration to show their solidarity with the presidential stance.
"Today we make the following appeal to the president of this country who has all legal grounds to call an early election," Tymoshenko said while addressing the rally. "It is not just the president's right to dissolve parliament. It is his duty to dismiss this corrupt, treacherous assembly and go ahead with an ho open, honest early election in which there can be no doubt democratic forces, those who defend and love Ukraine, will win."
A smaller crowd of supporters of the ruling coalition headed by Prime Minister Viktor Yanukovych, who is seen as friendlier to Russia, held a separate rally on a square just hundreds of meters away.
Yanukovych argued that there are no grounds to dissolve parliament, and that the president's ultimatum should be ignored.
"We will never accept ultimatums that are outside the realm of law and the constitution," Yanukovych told the crowd. "I have said this repeatedly."
Yushchenko has accused the pro-Russian coalition that dominates parliament of illegally attempting to expand its majority by persuading lawmakers from blocs that support the president to switch sides.