Ms Yingluck made her plea after returning Sunday morning from a visit to Switzerland, Italy, the Vatican and Montenegro.
She said she had been updated on the situation, particularly the road blockades at Khuan Nong Hong intersection in Cha-uat district and Ban Tao Poon intersection in Chulabhorn district of Nakhon Si Thammarat, and instructed the national police chief to maintain law and order at the two spots.
Since the majority of rubber growers were satisfied with the subsidy of 2,520 baht per rai, capped at 25 rai, the minority should respect their decision, Ms Yingluck said.
If the farmers did not want to end the blockades, they should act within the scope of the law, Ms Yingluck said.
In Nakhon Si Thammarat, the protesting rubber farmers issued a statement demanding the government guarantee the prices of raw rubber sheet at 120 baht per kilogramme and oil palm at seven baht per kilogramme and for Ms Yingluck to attend every meeting of the House of Representatives.
They vowed to continue with the protest and road blockades if their demands were not met.
The statement said if the government wanted to negotiate with the farmers it should send representatives to meet them in Nakhon Si Thammarat because they would not travel out of the province for talks.
The blockades came after a rift emerged among rubber and palm oil representatives from 14 southern provinces. They were split into two groups, with one signing an agreement over the 2,520 baht per rai subsidy offer.
Farmers from five provinces - Nakhon Si Thammarat, Songkhla, Pattani, Yala and Narathiwat - agreed to sign the subsidy deal with Thawach Boonfueang, deputy secretary to the prime minister, who met farmers' representatives at a hotel in Nakhon Si Thammarat's Muang district on Saturday.
A survey by the Abac Poll shows that many respondents believed that the rubber farmers' protest poses the highest risk to the country's political stability.
The study involved 2,235 respondents in 17 provinces nationwide.
A score of zero to 10 is used with 10 representing a high level of risk. The rubber farmers' protest received 8.80, followed by corruption and politicians' behaviour at 7.88, economic issues at 7.81, the 2.2-trillion-baht borrowing bill at 7.38, and the amnesty bill at 7.34.
Ms Yingluck's popularity as prime minister received a score of 6.67 out of 10.
Meanwhile, a group of people reportedly gathered in front of the VIP lounge at Suvarnabhumi Airport on Sunday morning, raising banners attacking the premier for travelling too frequently on overseas trips.