There are 390 words in a 3-minute speech for someone with an average speech rate of 130 words per minute. The number is dependent on how fast the person speaks.
A slow speaker averages 100 words per minute, so a 3-minute speech for a slow speaker requires about 300 words. In comparison, a fast speaker averages 160 words per minute, so to achieve a 3-minute speech, a fast speaker requires 480 words.
The most accurate way to know how many words are needed is to practice and record a speaker's speech rate. Then, either adjust the speech rate so it is slower or faster, or change the word count to accommodate the 3-minute time limit.