``We have full faith in the prime minister,'' declared Labor Minister Mahinda Samarasinghe, quoting from a a letter signed by 124 of the nation's 225 MPs.
Chandrika Kumaratunga did not say what action her government would take if the Tigers did not respond to her two-week deadline.
The "message" was given to Norwegian Foreign Minister Jan Petersen during his meeting with LTTE chief Velupillai Prabhakaran.
Sri Lanka's Supreme Court ordered presidential elections by the end of the year.
But no party managed to cross the magic number of 113 needed to enjoy an absolute majority in the 225-member legislature, pointing to either a minority government or a shaky coalition.
"We will leave the government if the President does not withdraw the joint mechanism plan with Liberation Tigers of Tamil Eelam by June 15," the Marxist Janatha Vimukthi Peramuna or People's Liberation Front said.
The prime minister, however, made it clear that he will not discuss the president's proposal to form a government of national unity.
The government wants to test public opinion before going in for drastic constitutional changes, officials said.
Wickremesinghe is the first Sri Lankan president to be elected by Parliament following a vote.
External Affairs Minister Sushma Swaraj on a two-day visit during which she is expected to discuss the fishermen's issue and rights of minority Tamils with the Lankan leadership.
Sri Lanka President Mahinda Rajapaksa has debunked international criticism over the treatment of the island nation's Tamil minority population.
Maithripala Sirisena, Sri Lanka's president-elect, was a low-profile cabinet colleague of longtime president Mahinda Rajapaksa until he switched sides to become joint opposition candidate and emerge as the proverbial dark horse in the presidential polls.
Few debut novels in recent times have been received with such critical applause as Akil Kumarasamy's Half Gods. 'The prose itself is a marvel,' declared The New York Times Book Review. A glimpse of Akil Kumaraswamy's ability to 'distill the mysteries of the human soul', revealed in this excerpt from her story The Office of Missing Persons.
Maithripala Sirisena was considered so meek and self-effacing that he appeared no threat to anyone. What a mistake his rivals made!
Voicing concern over violent non-state actors controlling large territories across the world and unleashing "barbaric violence", Prime Minister Narendra Modi on Thursday said that ideologies should give way to dialogue to resolve conflicts.
The country has a fiendishly complicated electoral system that is a combination of population-based proportional representation and party-based national lists, says Aditi Phadnis
'We should expect a cold-blooded, transactional relation that requires a lot of engagement and mutual trust to sustain,' says Constantino Xavier, Fellow, foreign policy, Brookings India.
'As I went around Batticaloa, Trincomalee, Jaffna and Mannar, my mind went back to my visit in January 1990 at the fag end of the IPKFs mission in Sri Lanka,' says Colonel Anil A Athale (retd).
The two countries also signed memoranda of understanding in education and health sectors after visiting External Affairs Minister Sushma Swaraj and her Lankan counterpart Mangala Samaraweera co-chaired the 9th Indo-Lanka Joint Commission meeting in Colombo.
Former RA&W chief A S Dulat, who served as Atalji's adviser on Kashmir, gives us an insider's glimpse of a prime minister he has hailed as the 'greatest after Nehru'.
As the island heads for elections, two major factors worry Sri Lankan President Mahinda Rajapaksa. One is the division in the Sinhala vote and the other is the prospect of the Tamils and Muslims voting heavily against him.