By Tom Gibb
BBC News, Sao Paulo
Some 10,000 to 15,000 Brazilian students and trade union members have marched through the capital, Brasilia, in support of the embattled president.
Students and unionists want to keep Lula and fight corruption
Luiz Inacio Lula da Silva is embroiled in a deepening corruption scandal that hit his ruling party in June.
The protesters called for changes in government policy and punishment for those responsible for corruption.
But they also said they supported the continuation of the Brazilian president in office.
This was the first big public demonstration since the corruption scandal broke.
It was organised by trade unions which Brazil's president, the former factory worker known as Lula, used to lead.
For months now, Brazilians have been hearing accusations that Lula's Workers' Party paid allies to support them in Congress and used undisclosed campaign funds.
The scandal has deepened divisions in Brazil's left wing, which was once united in its support for Lula.
This protest demanded political reform to stop corruption, but it opposed the impeachment of Lula himself, which some opposition leaders now want.
By contrast, another protest due on Wednesday by left-wing groups which had broken away from the government is expected to demand that Lula step down.
The level of protests may become important, with some opposition congressmen saying they will only support impeachment if the public demands it.
While opinion polls have shown Lula's popularity falling badly, they have also so far shown that most Brazilians do not want to see him impeached.