Hi Victoria,

   I agree with Laurence, and want to add more to that. Recently I was trying to design primers specific for certain taxa and successfully did that. Non of the current free primer designing soft wares are really good for this purpose. However the best one as per my experience is AlleleID (http://www.premierbiosoft.com/bacterial-identification/index.html). It aligns the sequences of the species of the same genus as well as the related genus and takes the unique (yet conserved among different species of the same genus) sequence of the genus for primer designing. However you have to do little manual changes in the primer sequences (mostly 5' side) to fulfill all other parameters of the primer.

Primer3 with sequences do

Hello Victoria. I am not aware of primer design software should specifically for making genus wide primers. 

The best I can suggest is selecting a region that is common to all such species using NCBI BLAST and then taking that common region and designing primers using primer blast; both functions are aspects of NCBI Genbank: 

https://blast.ncbi.nlm.nih.gov/Blast.cgi

Hi Victoria,

   I agree with Laurence, and want to add more to that. Recently I was trying to design primers specific for certain taxa and successfully did that. Non of the current free primer designing soft wares are really good for this purpose. However the best one as per my experience is AlleleID (http://www.premierbiosoft.com/bacterial-identification/index.html). It aligns the sequences of the species of the same genus as well as the related genus and takes the unique (yet conserved among different species of the same genus) sequence of the genus for primer designing. However you have to do little manual changes in the primer sequences (mostly 5' side) to fulfill all other parameters of the primer.

Much obliged for the last answer. It's always good to learn something new 

Thank you so much, it's exactly what I needed. Thank you all for your answer.