One of Susilo's major political allies in the country's fractured parliament, the Prosperous Justice Party, also criticised the price increases, saying the government had yet to work out a detailed plan to compensate the poor.
News radio station El Shinta and the official Antara news agency reported student protests and strikes by public transport drivers in at least 10 cities across the country.
On Tuesday, hundreds of students blocked roads in the city of Makassar in the country's east, El Shinta said. In Jakarta, they burnt tyres near a key intersection and shouted slogans accusing Susilo of failing to defend the poor, witnesses said.
The authorities have placed security forces on alert, with protests expected to escalate during the day. The largest demonstrations so far have involved several hundred students.
Aljazeera's Indonesia correspondent, Usman al-Batiri, said the protests in Indonesia had yet to have any major impact as there were few protesters in the streets.
But he said things could change if the students received backing from political parties.
Officials late on Monday announced domestic fuel prices would rise an average of 29%. The increases cover items such as petrol and diesel, and took effect in the early hours of Tuesday.
Petrol prices are now 25 US cents (2400 rupiah) a litre, still by far the cheapest in Asia. In Asia's other big oil exporter, Malaysia, which also moved on Monday to cut fuel subsidies, unleaded petrol costs about 37 US cents a litre.
Tyres were burnt in street
protests around Indonesia
Phased cuts of subsidies in the past have sparked violence and forced previous presidents to roll back some price increases.
Susilo, Indonesia's first directly elected president who took power in October, said last week he was ready to become unpopular by sticking to the plan, but with a small support base in parliament, he could feel the political heat if protests get out of control.
Under pressure from foreign donors, former president Suharto sharply raised fuel prices in 1998, sparking huge street protests that contributed to his downfall that year.
Susilo told Indonesians on Monday the price hike was a bitter but necessary step. Economists have welcomed the decision, saying Indonesia needs to free up funds for infrastructure and development spending.
The subsidies last year cost the state $7 billion. Officials said the cuts would mean a fuel subsidy bill for the state this year of $39.8 trillion - still 10% of its budget expenditure.
Indonesia is Asia's only member of the Organisation of the Petroleum Exporting Countries, but was a net crude oil importer in certain months in 2004 due to production problems and low investment.