Ms Yingluck's call was made in a statement broadcast over the Television Pool of Thailand at 2pm.
The prime minister asked foreign countries to have confidence in Thailand, saying the government will adhere to peaceful means in dealing with the protesters.
She said although the protesters have occupied several public offices the government has plans to ensure public services will continue without disruption.
"The government does not want to play a political game because doing so will only cause the economy and the country to step backward," Ms Yingluck said.
On the protesters' call for the establishment of a "people's government", Ms Yingluck said her government cannot respond to it because it is not possible under the present constitution.
Protest leader Suthep Thaugsuban has called for a "people's government" as part of his six-point plan for reform.
The prime minister said she therefore called for the protesters to end their demonstrations and return the public offices they have occupied to the government.
She said the government will open a forum for talks for all concerned to attend to together find a way out of the political conflict.
As His Majesty the King's birthday is drawing near, she called for all people to heed the King's advice for them to love one another and unite.