The meeting comes in wake of Singh making clear to Shettar last Friday not to compromise on the BJP's principles even if it threatens the survival of the government in the southern state.
The party has, however, claimed that it is confident of overcoming the crisis.
Thirteen MLAs loyal to Karnataka Janata Party chief Yeddyurappa had gone in a delegation last Wednesday to meet Speaker K G Bopaiah to submit their resignation from Assembly membership.
As Bopaiah was not present, they had later submitted copies of their resignation letters to Governor H R Bhardwaj.
In the 225-member Karnataka Assembly, BJP has a strength of 117 excluding the Speaker and requires 113 for a simple majority. Congress has 71 members and JDS 26. There are seven Independents and two vacancies. One member is nominated.