"I have been asked by the party to stay and face this situation," Wickremesinghe said.
He had been expected to attend an information technology meeting in New Delhi, his officials said.
The Sri Lankan premier is currently battling calls for his sacking following the defeat of his United National Party.
Former president Mahinda Rajapaksa's supporters have demanded that President Maithripala Sirisena sack Wickremesinghe and appoint a government of the president's Sri Lanka Freedom Party.
The SLFP is said to be working to acquire a parliamentary majority on its own to oust Wickremesinghe from the ruling alliance.
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