The consulate said via Twitter it was monitoring the security situation and imposed an earlier evening curfew.
Late Thursday, the Tamaulipas state security coordinating group said a state police officer was killed when a convoy of police arriving from the state capital to bolster security was attacked in Nuevo Laredo. Another officer was wounded.
On Wednesday, the consulate issued a security alert saying it had "received reports of multiple gunfights throughout the city of Nuevo Laredo." It told U.S. personnel to shelter in place.
Tamaulipas Gov. Francisco Cabeza de Vaca blamed what he called "cowardly attacks" by the Northeast cartel via Twitter Wednesday. He said the state would use all of its tools to confront criminals.
Nuevo Laredo is one of seven Mexican border cities where the U.S. government returns asylum seekers to wait out their U.S. cases. It is firmly in the grip of the Northeast cartel, a faction of the Zetas.
On Wednesday afternoon, state police on patrol were attacked by gunmen, according to a statement from the state security coordinating group. Shots were also fired at a hotel that state police use as a barracks. One officer and a civilian in a nearby convenience store were wounded in the shootings.
Later, two people were killed at a hospital in Nuevo Laredo and a woman identified as a civilian outside it, according to the statement. Authorities later clarified that the two people killed at the hospital had been in a car outside it that was hit by gunfire and caught fire.
In another attack Wednesday, state police again came under fire, wounding one officer and leaving three gunmen dead, authorities said.