Both calls came in shortly before 9:30 p.m.
One of the incidents happened on 41st Street and 8th Avenue, where a group of men got into a fight outside a restaurant across from the Port Authority Bus Terminal.
One of them was armed with a tire iron, and at least one other had a knife.
Three victims were rushed to Bellevue Hospital. Two of them were seriously injured, while the other had a minor injury.
Two other people were stabbed on 46th Street and 6th Avenue. Their conditions are not yet known.
Police are trying to determine whether one person ran from the scene of the first stabbing and was involved in the incident at the second location.
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