Some joined protest leader Suthep Thaugsuban on foot and others followed in cars and six-wheel trucks as Thailand's long-running political conflict showed no sign of ending. (Agencies)
Others surrounded a government office in north Bangkok, where Yingluck was holding a meeting.
The protesters closed camps at two of the seven big intersections that Suthep's supporters have blockaded since mid-January, at Victory Monument and Lat Phrao, and were heading for the fringes of the central oasis of Lumpini Park.
A third camp run by an allied group at a huge government administrative complex may also be closed.
Suthep said on Sunday this was being done out of safety concerns, but it could also be because their numbers are dwindling. Reuters put the number of marchers at about 3,000.
"Suthep's movement is now crumbling, but it still has powerful unseen backers," said Chris Baker, a historian and prominent Thailand scholar.
"Backdoor negotiations are needed because both sides will avoid any direct confrontation in public view. The business lobby should revive its efforts to play the intermediary role."
Suthep's supporters on the route showed no sign of crumbling, waving flags and handing over money.
The demonstrators blocked balloting in a fifth of the country's constituencies on Sunday, saying Yingluck must resign and make way for an appointed "people's council" to overhaul a political system they say has been taken hostage by her billionaire brother and former premier, Thaksin Shinawatra.
The election, boycotted by the main opposition party, is almost certain to return Yingluck to power and, with voting passing off peacefully across the north and northeast, Yingluck's supporters will no doubt claim a legitimate mandate.
But the vote is unlikely to change the dysfunctional status quo in a country popular with tourists and investors yet blighted by eight years of polarisation and turmoil, pitting the Bangkok-based middle class and royalist establishment against the mostly poor, rural supporters of the Shinawatras.
Some joined protest leader Suthep Thaugsuban on foot and others followed in cars and six-wheel trucks as Thailand's long-running political conflict showed no sign of ending.