The beleaguered president added that he had asked his popular Vice-President Megawati Sukarnoputri to take a greater role in the running of the government.
Speaking following a cabinet meeting, Mr Wahid said he had no intention of stepping down and wanted to "maintain this country's integrity".
The beleaguered president added that he had asked his popular Vice-President Megawati Sukarnoputri to take a greater role in the running of the government.
Pressure is growing on Mr Wahid, who is beset by corruption allegations and has faced a series of crises in recent months.
At least 10,000 students took part in the demonstration but their call for a general strike appears to have gone largely unheeded.
Security threat
Although shops and offices remained open, the demonstration is said to have led to a fall of more than 10% in the value of the Indonesian currency, the rupiah.
Anticipating violence, Jakarta police said they would do what they could to prevent "anarchy" and deployed 4,000 officers at strategic points in the capital.
Security forces moved swiftly to stop minor skirmishes which broke out between pro- and anti-Wahid demonstrators.
Some protesters carried an effigy of the embattled president bearing the phrase "stop talking, just resign", which they said they would burn outside the palace.
"We have come to the conclusion that Wahid must go... the country is in a sorry state," said student union leader Taufik Riyadi.
Fuel rises
Student leaders said the protests were also against the government's planned rise in fuel prices next month.
President Wahid has been under pressure to resign and hand power to Mrs Sukarnoputri, since he was censured on 1 February for his alleged involvement in two financial scandals.
His opponents have also accused him of failing to carry out reforms, end violent separatist and communal conflicts and take the country out of its economic doldrums.