Yemeni President Ali Abdullah Saleh on Thursday expressed his deep regret over the opposition's insistence on organizing constant protest rallies against him, a day after he promised to stand down in 2013 and not to hand power over to his elder son.

"I hope my meeting on Wednesday with the members of the Parliament, consultative Council and the military as well as the initiative I offered to the opposition would eradicate the tension between us and them," Saleh said in address aired by the country's state television this evening, hours after more than 20,000 supporters of the opposition struck streets of the capital Sanaa demanding his ouster.

"The opposition gave no ear to our initiative, insisted to organize anti-regime protest rallies," he said as the opposition coalition also organized dozens of rallies across other major cities which thousands of protesters attending.

In his speech to the nation, Saleh repeated his offer for dialogue with the opposition.

"Again, I'm ready to sit down at the table of dialogue together with my brothers in the opposition and I ask them to keep away from tension and agitation," Saleh said, stressing that " dialogue is the best way to the country's political crisis."

Earlier Thursday, over 20,000 Yemeni protesters struck the streets of Sanaa for a "Day of Rage" march, demanding clearly to oust President Saleh.

"The people want the regime to fall, the people want President Saleh to leave," angry protesters shouted in the largest popular rally outside Sanaa University while thousands of ant-regime tribesmen joined the crowd.

"The people want freedom," protesters chanted in row of lines wearing pinky belts on their heads.

President Saleh, facing growing demands to leave power, announced Wednesday he would not seek another term or hand over power to his son, and said he has frozen the ruling party's controversial amendments, which proposed to allow him to be the country's president for life, adding he postponed next parliamentary elections to meet all the demands of the opposition.

Saleh also called the opposition to cancel the mass protest that has already took place on Thursday.

However, the opposition said on Wednesday that they will go to the streets to demand more reforms.

Mohammed Abdulmalik al-Mutawakil, the head of the opposition coalition told Xinhua that "he met with the president two days ago and agreed to direct the opposition protest rally not to demand the ousting of Saleh, but things get out of controls. The protesters clearly demand Saleh's ouster."