(Adds police estimate of number of protesters)
SANTIAGO, March 22 (Reuters) - Tens of thousands of protesters marched in Chile on Saturday to press center-left President Michelle Bachelet to follow through with ambitious reforms she pledged before assuming power less than two weeks ago.
The protest in downtown Santiago, dubbed "the march of all marches," was the first of Bachelet's new term and the biggest political demonstration in the world's top copper exporter since massive student protests in 2011.
Police said there were 25,000 protesters but organizers of the march said at least 100,000 people turned out, even without core groups of student protesters active in the past.
Those activists said they would not take part because they are working with Bachelet on an education reform package that will soon be sent to Congress.
The march underscored lingering frustrations in Chile and higher expectations following four years of unpopular conservative former president Sebastian Pinera.
Protesters said the march was a warning sign they would not go easy on the new president of Chile, where a decade-long mining boom has not closed a wide inequality gap.
"This is not a protest against Bachelet or for her, it's just an alert for the political class so they know people have demands," said Oscar Rementeria, a spokesman for gay rights group Movilh.
The 40 activist groups that helped fill the streets supported causes ranging from environmental protection to gay and indigenous rights.
Protesters also voiced support for a new constitution to replace the one in place since Augusto Pinochet's 17-year dictatorship. Bachelet has backed a new constitution.
Returning to Chile's top job after a spell with the United Nations, Bachelet has said she wants to address social inequality by overhauling education and healthcare, funded by tax reforms. (Reporting By Felipe Iturrieta, Writing by Mitra Taj; Editing by David Gregorio and Diane Craft)