Adds fresh police quotes, Obama reaction, details (the first version was posted at 17:20)
An Israeli woman was killed and at least 39 people were injured in the first bomb attack in Jerusalem in more than six years.
Three of the injured were in a serious condition, a spokesman for the Magen David Adom ambulance service told the German Press Agency dpa.
The bombing was the first suspected Palestinian attack in Israel's unrecognized capital in two years, and the first bomb to explode in the city since 2004.
No group has claimed immediate responsibility for the attack.
But police spokesman Micky Rosenfeld said authorities were working on the assumption that Palestinian militants were behind the bombing.
"As far as the police are concerned it was a terrorist attack," Rosenfeld told dpa.
He said this was clear from the busy location chosen, and from the type of bomb, which contained screws and bolts to cause as much damage as possible - as has been typical in past Palestinian suicide bombings.
The explosive device had been placed in a bag next to a bus shelter opposite the city's central bus station. It exploded as two packed buses were passing.
It weighed between 1 and 2 kilograms, Minister of Public Security Yitzhak Aharonovich told reporters.
Prime Minister Benjamin Netanyahu postponed a scheduled trip to Russia until late in the evening.
Both Palestinian President Mahmoud Abbas and Acting Palestinian Prime Minister Salam Fayyad strongly condemned what they termed a "terrorist act."
US President Barack Obama also condemned the bombing "in the strongest possible terms."
"There is never any possible justification for terrorism," Obama said in a statement.
He also expressed condolences for the recent deaths of Palestinian civilians in Gaza by a volley of Israeli mortar shells.
"This obligates a response," Israel's interior minister, Eli Yishai of the ultra-Orthodox Shas party, said of the bombing. In the absence of a response, Israel's "power of deterrence" would be damaged, he said.
Police closed the scene to traffic and forced onlookers to move on, while sappers combed the area for any possible additional hidden explosives.
The last bombing in Israel occurred in February 2008, in the southern desert town of Dimona - near the country's nuclear research centre. One Israeli and two Palestinian suicide bombers were killed on that occasion.
In March 2009, a Palestinian resident of occupied East Jerusalem ran amok with a bulldozer. The man, who had tried to run into a police car, was shot dead by a passerby.
That attack came after three bulldozer attacks the previous year in which three Israelis were killed.
But the last suicide bombings in the city took place in 2004.
"This is the first event after many, many years," National Police chief David Cohen told reporters.
Police have raised the security alert level as a result, and would deploy in "very large" numbers on Friday, when Jerusalem holds its annual marathon. Under no circumstances would the event be cancelled, Cohen said.
The Gaza Strip and southern Israel have in recent days seen a resurgence of deadly violence in the form of Palestinian rocket and mortar attacks and Israeli retaliatory strikes.
But the second Palestinian Intifada (uprising) had largely died down elsewhere in Israel and the occupied West Bank.
That uprising saw suicide bombings against Israel peaking in the mid-2000s.
Wednesday's bombing came after the worst violence in Gaza and southern Israel since the Israeli offensive in Gaza if the winter of 2008-2009.
On Tuesday, Israel killed eight Palestinians, among them four civilians, in two separate incidents in the deadliest single day in two years.
In the afternoon, Israeli troops on the border fired a volley of four mortar shells at al-Nazzas street on eastern Gaza City outskirts, after Palestinians militants fired from the area.
Four civilians, including three members of the al-Helou family, were killed, including two youths who were outside playing football. Another 11 civilians were wounded, among them eight children.
The Islamic Jihad in Gaza for its part fired three Grad rockets at two of Israel's largest cities in the south of the country with about 200,000 residents each, Ashdod and Ashqelon.