"Lawmakers have been haggling over the portfolio for weeks, forgetting about 48 million people," Viktor Yushchenko said.
The opposition Party of Regions, led by former presidential candidate Viktor Yanukovych, said earlier on Thursday it would continue its two-day sit-in to block the country's parliament until it was offered leading posts in the assembly.
The pro-Russia party, which won the largest share of votes in March 26 parliamentary elections but was frozen out of a coalition deal, has also been protesting against the coalition's intention to vote for Yulia Tymoshenko, an ex-prime minister and prominent figure in the 2004 "orange revolution", and Petro Poroshenko, a businessman and former secretary of Ukraine's Security Council.
Yushchenko said, "I call on all parliamentary forces to quickly gather at the talks table. I am fulfilling my role as president in regulating such a standoff, and will do this strictly in line with the constitution."
On the subject of the election of a speaker and of Tymoshenko as premier, the president said that these procedures must be carried out according to parliamentary and constitutional rules.
The Party of Regions leader said he was sure the coalition - comprising Tymoshenko's bloc, pro-presidential grouping Our Ukraine, and the Socialist Party - would never agree to his party's demands or make concessions, and said his faction would continue blocking parliament until the coalition "ceased to break the law".
Leaders of the three groups agreed to form a coalition majority in the Rada June 22 after months of political wrangling following elections in March. Members of Our Ukraine and the Socialist Party have said the opposition's demands should be partially met in order to allow the Rada to get down to work.
The Party of Regions is protesting in parliament for a second day. Yanukovych, beaten by President Viktor Yushchenko in the 2004 presidential race, said earlier: "We are prepared to block the parliament's work for 30 days if it is necessary."
The Supreme Rada, parliament, would have to be dissolved in 30 days if its members fail to hold a session.