New York officials are looking for Ahmad Khan Rahami, a naturalised US citizen who was born in Afghanistan for questioning over Saturday's blast in the Chelsea area of Manhattan.
The bomb injured 29 people and another unexploded device was found nearby. Early on Monday, a backpack containing up to five devices exploded in Elizabeth, New Jersey, when a bomb disposal robot tried to deactivate it. New York's governor said there were "commonalities" between the bombs.
The 28-year-old suspect's last known address was in Elizabeth.
FBI officials were searching a residence in the New Jersey city on Monday.
What we know so far
Investigators have warned that the suspect should be considered "armed and dangerous". Millions of New York residents received a phone alert on Monday morning after the Notify NYC alert system was used to name the suspect.
"Anyone who sees this individual or knows anything about him or his whereabouts needs to call it in right away," New York Mayor Bill de Blasio said on CNN.
Both the bomb that went off in New York on Saturday and the unexploded device found nearby were shrapnel-filled pressure cookers, according to US media.
New York Governor Andrew Cuomo said on Monday that there might be a foreign connection to the Manhattan attack. Officials had said over the weekend there were no confirmed links to international terrorist groups.
President Barack Obama, who is in New York for the United Nations General Assembly, is being kept up to date with the investigation, a White House spokesman said. The backpack in New Jersey was found near the railway station in Elizabeth.
It was picked out of a bin by two men on Sunday evening, who thought the bag could contain something of value. "That was not a controlled explosion," said Elizabeth Mayor Christian Bollwage, adding that the blast, in the early hours of Monday morning, happened as a robot examining a device cut a wire. No one was injured.
Also on Saturday, nine people were stabbed at a shopping mall in the US state of Minnesota, in an attack apparently carried out by a 22-year-old ethnic Somali.