Businesses, including fast-food chains, were shut in support of the protest.
The president is facing impeachment proceedings over the affair, which has seen his former deputy jailed and six cabinet ministers quitting in protest.
He has apologised over the scandal but denies involvement. He is due to step down at the end of his term in January.
Guatemalans are due to vote in just over a week's time to choose his successor.
Investigators have alleged that top government officials received a cut from bribes paid by businesses seeking to evade import duties.
The scandal has been dubbed "La Linea", or "The Line", after the hotline businesses allegedly rang to clear their imports through customs at cut-price rates.
United Nations-backed investigators have accused the president of direct involvement in the customs scandal.
In a televised address to the nation last week, Mr Perez Molina dismissed the allegations and insisted that his conscience was clear.
The former vice-president, Roxana Baldetti, has been arrested over her alleged involvement in the affair.
Prosecutors say she took a 50% cut from the bribes. She appeared in court on Wednesday, denying the charges.
On Thursday, marchers took to the streets of Guatemala City, waving placards attacking corruption in the political establishment.
"The country is bad. We have seen it, everything that has happened," a protester, Hegel Aquino, told the Reuters news agency. "What we want is his [President Perez Molina's] resignation," he said.
A committee has meanwhile been formed to consider lifting the president's immunity from prosecution.
The committee was created after the country's Supreme Court gave the the go-ahead for prosecutors to request impeachment proceedings.
Major business and religious leaders are supporting calls for the president to resign.
Thousands of protesters have marched in the Guatemalan capital, demanding the resignation of President Otto Perez Molina over a corruption scandal.