Rousseff made no comment after her meeting in the capital Brasilia, but in the wake of yesterday's protests, she is fighting for her political life.
Between one and three million people flooded the streets of Sao Paulo, Rio, Brasilia and some 400 other cities, according to conflicting data.
Turnout in Sao Paulo was estimated at 500,000 by the research center Datafolha and 1.4 million by the Sao Paulo military police.
The figures surpassed estimates by either organisation in previous opposition demonstrations.
The historic rebuff on the streets left Rousseff few options as another grueling week started, with Congress geared up to relaunch stalled impeachment proceedings.
An attempt to impeach the country's first female president began last year but fizzled out on technicalities.
On Wednesday or Thursday, the Supreme Court is expected to set out the rules, opening the door for Rousseff's many enemies in the legislature to ramp up the pressure.
Prosecutors indicate that his legal troubles are only just beginning, and there has been a request to a judge that he be put into preventative detention.
For Rousseff, this threatens a key ally.
Lula, who founded the ruling Workers' Party and was president from 2003-2010, is far more popular than Rousseff and gives her much of her credibility with the left-wing base.
Lula, who denies charges that he failed to declare ownership of a luxury seaside apartment, defiantly says that prosecutors have only spurred him into deciding on a comeback attempt as president when Rousseff's second term ends in 2018.
"I will be a candidate for the presidency in 2018, because I think a lot of the people who've been on my back will be getting the same treatment from me from now on," he said, according to a transcript released today.
