Our correspondent says demonstrators remained on the capital's main square through the night.
The rally began Thursday after Bakiev failed to observe a deadline to introduce measures that would curtail his presidential powers. Police in riot gear have been deployed around the presidential headquarters.
Protesters spent the night in around 200 small tents near government headquarters in the Kyrgyz capital, signaling opposition plans to maintain public pressure in the absence of any breakthrough over stalled constitutional reforms.
'No Reason To Worry'
Earlier Thursday evening, an estimated 15,000 or more protesters were gathered.
President Kurmanbek Bakiev told Russian state television after yesterday's protest was well under way that he saw "no reason" to worry for his government's stability.
Bakiev said he had enough "forces" at his disposal to cope with any potential unrest. He also suggested he had the support of the armed forces and of the majority of the population, "who wants to live and work normally."
By early evening Thursday, there had been no signs of violence as thousands gathered on the square around the government building to register discontent over a failure to move forward with promised changes to the system of government, according to RFE/RL's Kyrgyz Service.
Demonstrators and opposition leaders have demanded that Bakiev and his team usher in reforms or step down.
Police and national guard troops are on hand to quell any possible trouble, with memories of the ouster in March 2005 of long-time President Askar Akaev still fresh in Kyrgyz minds.
Most shops in the center of Bishkek were closed as businesses told employees to stay home. Even university activities were on hold as thousands of people crowded onto the Kyrgyz capital's central Alatoo Square.
Many estimates put the number of protesters at upward of 15,000, but the Interior Ministry said the crowds numbered no more than 7,000.
The demonstration's organizers distributed hot meals to those willing to stay overnight on the square. Tents were set up at the scene to provide demonstrators with shelter -- echoing steps from previous, far smaller, protests in the Kyrgyz capital.
Opposition leaders have said that the protest will go on until their demands are met.
Senior officials -- including the president and the other half of the ruling "tandem," Prime Minister Feliks Kulov -- resisted calls to address the protesters. But lawmaker Melis Eshimkanov and other opposition representatives met privately with Prime Minister Kulov at government headquarters after the protests began.
President Bakiev (right) and Prime Minister Kulov addressed a protest rally in April 2006
"Dear fellow countrymen!" Eshimkanov told the crowd outside the government building after that meeting. "In accordance with your assignment, [opposition deputy] Kabay Karabekov, [NGO leader] Cholpon Jakupova, and I came out from the 7th floor [of the government building]. We have negotiated with them. Feliks Kulov, together with other members of his government, negotiated with us. Feliks Kulov told us, 'I cannot quit the tandem. I cannot go out to address the crowd.'"
Bakiev's spokesman Nurlan Shakiev told RFE/RL's Kyrgyz Service late in the day that it was still unclear whether Bakiev would meet with the protesters.
"So far I don't have any exact information as to whether the president will go out and meet with participants to the rally," Shakiev said. "As far as I know, no decision has been made yet."
Roughly one-third of Kyrgyz lawmakers urged Bakiev and Kulov on November 1 to find a way out of the current standoff within 24 hours or leave.
The country's leading opposition movement, For Reforms, organized its protest to pressure President Bakiev to make good on reform promises or resign.
A small number of presidential supporters gathered early in the day for a counterdemonstration, vowing to keep Bakiev in the post that he took up shortly after the public uprising toppled Akaev in March 2005. But they appeared to have left by early evening.
Supporters of one of the opposition For Reforms movement's leaders, Omurbek Tekebaev, launched calls for the president's resignation at the outset of the demonstration at 2:00 p.m. local time Thursday. Many chanted "Bakiev, out! Bakiev, out!"
The For Reforms movement claims President Bakiev has failed to keep the promises he made to the country before his election in July 2005. Bakiev stepped into the breech after Akaev fled Kyrgyzstan and, during the weeks leading up to the special presidential election, made a number of promises -- including the adoption of a new constitution.
A former parliamentary speaker, Tekebaev told the crowd of protesters that it has a right to demand that the government fulfill its reform promises.
"Today is a historical day," Tekebaev said. "We came to remind the authorities of their promises and to insist they fulfill those promises. If we do not put pressure on them -- psychologically, morally, and politically -- they will not fulfill their promises. We have every right to do this. Reform!"
'Again The Thieves'
Roza Otunbaeva, who co-chairs another opposition party, Asaba (Flag), and served briefly as foreign minister after Bakiev came to power, was among the government's harshest critics at the rally. She claimed that all of the achievements of March 2005 have been undone by Kyrgyzstan's new government, whose headquarters are known as the White House.
"Less than two years ago, we stood here -- on this very spot," Otunbaeva recalled. "[And] we thought we had rid ourselves of all the thieves. But again the thieves are occupying the White House."
An appearance by President Bakiev in parliament ahead of the protest appeared to add fuel to the fire. Some deputies said they expected Bakiev to introduce a new draft constitution for debate -- one of the demands of the demonstrators outside the parliament building. Instead, the president vowed to present parliament with that document early next week -- then left out a back exit of the legislative building. Some of the protesters who spotted him reportedly jeered Bakiev as he left.
"On [November 6], I will personally -- with my own hands -- present a draft [constitution], I swear it," Bakiev told legislators in the morning session on November 2. "Please review the document for 10 days; but do not drag this out, because if parliament cannot adopt it, what can I do? I will have to hold a referendum."
Bakiev has issued the referendum challenge before to the legislature. He has also suggested he might seek to disband parliament if a compromise is not found, although he appears to have backed away from that threat.
A special commission made up of government and opposition members has drafted competing versions of a new constitution. One prescribes a parliamentary system of government, one lays out a presidential system, and another is a blueprint for a parliamentary-presidential system.
President Bakiev has made it clear that he prefers the version that preserves a strong executive branch, despite expectations from many that the new constitution would increase the role of the parliament.
Adding to the anxiety of those in charge of maintaining order is the knowledge that the crowd that chased former President Akaev from office a little over a year ago was far smaller than the number of people on Alatoo Square at the height of this latest protest.
(Ainura Aksanjoeva and Tynchtykbek Tchoroev of RFE/RL's Kyrgyz Service contributed to this report.)