Yushchenko issued the threat on March 29, accusing Yanukovych's ruling coalition of violating the constitution.
Addressing the rally in Kyiv today,Yanukovych accused the opposition of seeking to bring about early parliamentary elections "at any price."
"A small group of those disgruntled by the fact that they were not supported by the people and who found themselves outside the bodies of power have been trying -- almost since the early days following the [parliamentary] elections -- to bring closer the date of parliamentary elections at any price, in violation of the laws and the constitution of the country," he said.
Police say some 15,000 people took part in the rally.
Meanwhile, opposition leaders led by former Prime Minister Yuliya Tymoshenko appealed today to Yushchenko to call early elections.
The opposition also plans to hold a major rally in central Kyiv on March 31.
"We want the people to tell the president by coming [to the rally] that they want early elections to the Verkhovna Rada," Tymoshenko told reporters today. "And it seems to me that the president will also rely on society and on the public opinion. And everyone who will come to the square will be a voice in favor of early elections."