Thai Prime Minister Yingluck Shinawatra has rejected protesters' demands that she step down, amid ongoing clashes in Bangkok.

Ms Yingluck said the demands were not possible under the constitution, but that she remained open to talks.

More clashes broke out on Monday as protesters tried to storm the prime minister's office, Government House.

"Anything I can do to make people happy, I am willing to do... but as prime minister, what I can do must be under the constitution," Ms Yingluck said.

Anti-government demonstrators have been calling on Ms Yingluck to step down, with protest leader and former opposition politician Suthep Thaugsuban saying on Sunday that Ms Yingluck should resign within the next "two days".

According to the report however, the protesters want to replace the government with an unelected "People's Council", alleging Ms Yingluck's government is controlled by her brother, ousted leader Thaksin Shinawatra.