About 12,000 people rallied in central Seoul on Friday afternoon, police said, and more were expected to join later. On Thursday night, a crowd estimated by police at 25,000 staged a candlelight protest.
Organizers have pledged that rallies will continue nonstop though Sunday.
South Koreans have been taking to the streets to criticize Lee for his handling of the April agreement with Washington to allow imports of U.S. beef.
Protesters complain Lee has ignored their concerns about mad cow disease, behaved arrogantly and given in to U.S. demands.
"I will open my ears in a more humble attitude and listen to the people," Lee said in a speech Friday to commemorate Memorial Day, a national holiday. He did not directly mention the beef dispute.
Later Friday, presidential spokesman Lee Dong-kwan said all eight senior presidential secretaries - including himself - had offered to resign.
In South Korea, senior officials at times of crisis sometimes offer to step down to deflect or diminish criticism of an embattled leader.
It was not clear whether the president would accept the resignations.
Many South Koreans fear that the beef deal fails to protect the nation from mad cow disease by allowing beef from older U.S. cattle, considered at greater risk of the illness.
South Korea's government said last week it would begin allowing imports this week, but withdrew the plan at the last minute Monday, apparently fearful of a public backlash.
The government also said it has asked the United States to refrain from exporting beef from cattle 30 months of age or older. Still, it stopped short of directly asking Washington for a renegotiation of the deal and failed to calm public anger.
Public outcry against the beef pact has dominated politics in South Korea and backed Lee's new government into a corner.
On Thursday an opposition boycott of the country's National Assembly forced Lee to cancel a traditional opening speech at the legislature.
U.S. beef has been banned from South Korea for most of the past four and a half years since the first case of mad cow disease in the U.S. was discovered in late 2003. Two subsequent cases were found.
Scientists believe the disease spreads when farmers feed cattle recycled meat and bones from infected animals. The U.S. banned recycled feeds in 1997.
In humans, eating meat products contaminated with the illness is linked to variant Creutzfeldt-Jakob disease, a rare and fatal malady.