Yushchenko and Yanukovych were rivals during the 2004 presidential election.
In his address, Yushchenko said that over the past year, Ukraine had witnessed what he called a "dangerous tendency to usurp power."
He criticized a campaign by the majority to win over deputies defecting from Yushchenko's side as a "barefaced revision of the will of the Ukrainian voters, a breach of the constitution and a direct road to lawlessness."
Yushchenko also threatened to dissolve parliament and call an early election if attempts to "cool hotheads" in parliament did not succeed.
"As president I want to assure you that I will never allow the parliamentary majority to be reformatted in violation of the constitution," he said. "If any political forces believe they can claim 300 seats [in parliament] and they declare repeatedly that there will be a 300-deputy coalition in parliament, then we should make a political decision and call early parliamentary elections."
Yushchenko is facing mounting pressure to dissolve parliament and call early elections.
RFE/RL Belarus, Ukraine, And Moldova Report
SUBSCRIBE For weekly news and analysis on Belarus, Ukraine, and Moldova by e-mail, subscribe to "RFE/RL Belarus, Ukraine, And Moldova Report."