"The constant strategy of the terrorists is to look at ways to divide and create terror and make life difficult for the people of Iraq," Mark Fox, a spokesman for the US military in Iraq told reporters, saying military planners were studying the two incidents "carefully".
"The terrorists are planning to split Karkh from Rusafa," said a senior Shia minister, using Baghdad's ancient names for the west bank (Karkh) and the east bank (Rusafa).
"If they think they can split Karkh from Rusafa they are dreaming"
Saadi Ahmed, shop owner
"This has been the plan by terrorists and their political allies all along to try and drive Shia out of Karkh so they can split Baghdad in half."
On the other side of the divide, Mahmoud Mashhadani, parliament speaker and an outspoken Sunni politician, called the destruction of the Sarafiya bridge as a "conspiracy to isolate the two halves of Baghdad".
Sunnis now mainly live on the west side of the river and Shia on the east.
Although the Sarafiya bridge was built in the 1940s by the British, its destruction prompted eulogies in local newspapers, as if it was a repeat of the shelling of the fabled Mostar bridge, which became a worldwide symbol of Bosnia's 1992-95 civil war.
"Destroying the Sarafiya bridge is an attempt to break Iraq's unity and to polarise our society"
Saad Eskander, national library director
Saad Eskander, director of Iraq's national library and a historian, said blowing up Baghdad's bridges had been a military strategy to conquer and defend the city since ancient times.
Medieval rulers burnt Baghdad's bridges, and then laid wooden planks on top of boats roped together, to stop invading Mongols from sacking the city.
The US military, in its wars against Saddam Hussein, destroyed bridges in Baghdad to hinder troop movements.
"Destroying the Sarafiya bridge is an attempt to break Iraq's unity and to polarise our society," Eskander said.
"It is a message that Baghdad will soon become two Baghdads - one for the Shia and one for the Sunnis."
But for those who share childhood memories of swimming under the 453 metre long span as trains chugged along its railway tracks above, Baghdad bridges will never be severed.
"If they think they can split Karkh from Rusafa they are dreaming," said Saadi Ahmed, who runs a money exchange store.
"The terrorists are trying to destroy Baghdad's landmarks to erase our proud history of civilisation."