Both calls came in shortly before 9:30 p.m.
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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.
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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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