Architects Against Fascism (AAF) - a group which has emerged in the last fortnight - is fighting an online campaign to damage the BNP member's candidacy.
In an email petition the group talks about halting the return of 'Albert Speer' to the world of architecture.
AAF is understood to have had talks with campaign group Unite Against Fascism, which helped postpone RIBA presidential hustings planned for Liverpool last week.
Phillips, who is facing Sunand Prasad and Valerie Owen in the RIBA election, triggered outcry 10 days ago when he was forced to admit his membership of the far-right BNP.
He has faced a barrage of criticism following this admission, with some campaigners calling for him to withdraw his candidacy.