Thailand's governing Pheu Thai party is urging the thousands of protesters in central Bangkok to end their demonstration and take their complaints directly to government ministers.

Anti-amnesty protesters have crowded onto Bangkok's Ratchadamnoen Avenue since the Senate rejected on Monday the controversial amnesty bill.

If passed, it would have paved the way for disgraced former Prime Minister and Pheu Thai leader Thaksin Shinawatra to return to the country from self-imposed exile after being found guilty of financial corruption while in office.

The Pheu Thai government -- led by Thaksin's younger sister Yingluck as prime minister -- piloted the bill through the lower House of Representatives. She had hoped the 149-seat Senate would pass the legislation, although she said last week her government would respect the Senate's decision.

The Senate rejected the bill 140-0 on Monday, but street protests continued -- up to 10,000 people, The Bangkok Post reported.

Chairman of the Pheu Thai Party Apiwan Wiriyachai said the ruling coalition had promised the public it wouldn't resurrect the bill and called for protesters to end their demonstrations, the Post reported.

Apiwan also criticized former Democrat Party Member of Parliament and rally leader Suthep Thaugsuban for calling for nationwide strikes and civil disobedience.

Suthep and other leaders of anti-government groups should hold talks with the government, Apiwan said.

The Post also reported that the Anti-Thaksin Coalition submitted a petition to the palace asking the king to allow a "people's council" to replace the government.

Around 3,000 members of the coalition comprising civic groups from 77 provinces marched to the Grand Palace alongside other anti-government groups.

The government's problems began when they introduced the proposed legislation into the lower house, sparking large street demonstrations against the bill.

The amnesty would have applied to offenses committed during and after Thailand's bloodless 2006 coup, which ousted Thaksin. He now lives in Dubai from where his critics say he wields political power through his sister.

Yingluck argued that the legislation is essential for reconciliation after years of political unrest that included the occupation by anti-government protesters Bangkok's main airport in 2008.

Protesters took to the streets of Bangkok for two months in 2010, but clashes with police and security forces left about 90 people dead.

The main opposition Democrat Party and human rights groups said the bill would have allowed abuses of civilians by security force to go unpunished.

Former Democrat Party Prime Minister Abhisit Vejjajiva also denounced the proposed legislation, despite the fact it could have afforded him amnesty.

The Department of Special Investigation and the Office of the Attorney General announced this month they would indict Abhisit and Thaugsuban -- Abhisit's former deputy prime minister -- for alleged murder and attempted murder for their roles during the 2010 demonstrations.

Abhisit, who lost to Yingluck in the election of July 2011, said Yingluck wanted to roll back her brother's prison sentence for corruption to pave the way for his return to Thailand.

The Nation newspaper reported that Thaksin had instructed the Pheu Thai Party to cling to power in the hope the anti-government demonstrations would die down soon.