At least six people have died in the violent clashes which erupted overnight between police and citizens protesting against Mr Widodo securing a second term following last month's general elections. Police sirens blared as fresh skirmishes broke out on Wednesday evening with thousands of protesters chanting and waving Indonesian flags in the heart of the capital.
Subianto, an ultra-nationalist politician, has refused to accept the official results of the April 17 election and instead declared himself the victor.
Protesters on Wednesday threw fireworks and rocks at the police, who responded by firing tear gas, rubber bullets and water cannon. At least three officers were injured in the clashes and carried away, an AFP reporter on the scene said.
Dozens were arrested and parts of Jakarta were littered with debris and burned-out cars, as the violence triggered security advisories from the US and Australian Embassies.
Rudiantara, the communications and information technology minister, said social media including Facebook, Twitter, and WhatsApp will be restricted on a temporary basis to prevent the spread of hoaxes and inflammatory content.
Of the six dead, one died of blunt force trauma, said a Jakarta hospital doctor, while a news website quoting a doctor at another hospital said one man died of bullet wounds.
The 67-year-old has appealed for calm and said he would pursue legal channels to contest the results, as he did, unsuccessfully, against Widodo in 2014. An ambulance filled with stones was found by police and dozens of people carrying envelopes of money when they were arrested.
Crowds supporting Subianto echoed the losing candidate's allegations of election fraud, gathering outside the Elections Supervisory Agency's headquarters in the center of Jakarta.
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Elsewhere, smaller poll protests were held in Sumatra's Medan city this week and in Pontianak on Borneo island, where more than 500 demonstrators armed with stones and firecrackers blocked roads, damaged vehicles and set two police posts alight, local police said.
Flanked by the military chief and other top leaders, a grim-looking Widodo said, "I will work together with anyone to advance this country, but I will not tolerate anyone who disrupts the security, democratic processes, and unity of our beloved nation".
Prabowo called for peaceful protests and restraint.
"Trust in your leaders".
"Avoid areas where demonstrations are occurring & exercise caution in the vicinity of any large gathering", the U.S. embassy said on Twitter. The soft-spoken Widodo - who pointed to his efforts to boost Southeast Asia's biggest economy with a huge infrastructure push - stood in stark contrast to Subianto, a fiery strongman who courted Islamic hardliners and promised to boost military and defence spending.
Election officials and analysts have discounted Subianto's claims of rampant cheating in the world's third-biggest democracy, after India and the United States. "We came here to demand justice because there was fraud in this presidential election", protester Mato told AFP. "We don't want chaos, but that depends on the police". Many residents have left the city and parts of the downtown are closed to traffic, with the election supervisory agency and Election Commission barricaded with razor wire.
Muhammad Iqbal, a police spokesman, said that the "majority of protesters have come from outside Jakarta" and that the protests had been planned, and were not spontaneous.