The two largest proxy-advisory firms are recommending that General Electric Co. fire KPMG LLP as its auditor after 109 years, in light of accounting issues at the industrial giant.

Institutional Shareholder Services made the unusual move on Thursday, saying shareholders should vote against keeping KPMG because of “the apparent extent of GE’s previously-undisclosed liabilities and accounting issues.” Glass, Lewis & Co. published a similar recommendation on Tuesday.

Earlier...