A 30-member delegation led by the TRS chief left for the national capital on Friday to meet Prime Minister Manmohan Singh.
The TRS chief has warned that the agitation on the issue will continue till the goal is achieved.
He also questioned the government's stance to hold "further consultations" on the issue.
The protest came even as senior Congress leader Ghulam Nabi Azad said in Hyderabad that the issue would be settled soon.
Rao and his supporters observed silence for a few hours at Rajghat, the memorial of Mahatma Gandhi in central Delhi, on the occasion of Gandhi Jayanti to highlight the "grave situation" in the Telangana region of Andhra Pradesh.
"We've been requesting the government to come forward and it is up to them to take a decision. We are not going to stop this movement or strike till we achieve Telangana state," KCR said.
The TRS alongwith the Telangana Joint Action Committee (TJAC) members were present at the protest. The members joined the prayer meeting held at the memorial of Gandhi, before speaking to mediapersons.
Asked if the Congress-led United Progressive Alliance government had requested for more time to take a decision, Rao said, "Do they think we are ignorant? How long are they going to cheat us? What more discussion do they want? (In) what way is our demand complicated?"
Rao, who has been camping here since Friday, said the government had made a promise in parliament. "What is the state of democracy? This will bring shame to the country." Rao accused the government of trying to provoke them to adopt violent methods of protest.
"From here (Rajghat), we want to give a message, we have been silent, democratic and non-violent all through and we will continue in the same way and would not be affected by the provocation," he added.
Asked how long the movement for a separate state would continue, the TRS leader said, "As long as the government of India keeps mum, this movement will continue."
TRS legislator KT Rama Rao said, "We are planning to meet the Prime Minister and his cabinet colleagues and probably the core committee members because they are the ones who make the decisions."
"I want to remind you that when it came to Jan Lokpal Bill, the government said that whatever is said on the floor of the house is supreme. Now why does not the same logic apply to us as well?," he asked.
In Hyderabad, Azad said consultations with the elected representatives of all three regions of Andhra Pradesh -- Telangana, coastal Andhra and Rayalaseema -- were completed but there was need for more consultations on the issue at the national level.
"We need more consultations at the national level. I would not be able tell you the exact date but we will try to settle this issue as soon as possible."
"We are also conscious of the situation. Lots of people are suffering because of the strike. I can't say we will do it tomorrow or day after but we are trying to settle the impasse as soon as possible," he added.
Azad appealed to government employees in Telangana to call off their strike, saying it was causing inconvenience to people.
"I am appealing to government employees in Telangana who are on strike for 20 days to withdraw the strike and cooperate with the people, especially in view of the festivals," he said.
The union minister said the strike had led to electricity shortage and hardships for farmers. He said labourers were hit hard as they were not getting work due to the strike.
Finance Minister Pranab Mukherjee said Saturday that the government was aware of the "gravity" of the ongoing agitation in Andhra Pradesh's Telangana region and needed "some more time" to find a solution to the vexed issue.
Congress leaders from Telangana are also pressing their leadership for an early decision in favour of creating a new state.
