The strength of Goa Assembly has reduced from 40 to 37 after the death of D'Souza and resignation of two MLAs -- Subhash Shirodkar and Dayanand Sopte.
While the Congress currently has 14 MLAs, down from 16 after Sopte and Shirodkar left it to join the BJP, the latter has 13 MLAs.
Three MLAs each of the Goa Forward Party, MGP and an Independent and the lone NCP legislator are supporting the BJP.
In a communication to the governor, Kavlekar said, "Consequent upon the sad demise of Francis D'Souza, MLA who was belonging to the BJP, it is humbly submitted that incumbent BJP led state government under the leadership of Manohar Parrikar, which has long lost the trust of the people, has also lost the strength of the House".
"Also, we anticipate that numbers of the BJP may further dwindle thus not allowing such a party in minority to continue even for a moment," his letter stated.
"It is therefore incumbent upon you to dismiss the state government led by the BJP and ensure that the Indian National Congress party, which is the single largest party in the House and is presently enjoying the majority, be called to form government," his letter added.
His letter warned that "any action in violation of the constitutional mandate to invite the single largest party to form the government and any attempt made to bring the state under President's Rule will be undemocratic, and illegal and will be challenged, as deemed fit".
"We are therefore staking our claim to form the state government and demand that we be called to form the government forthwith by dismissing the incumbent BJP led government," the letter read.
Bypolls to the seats previously held by Sopte, Shirodkar and D'Souza are to be held along with Lok Sabha polls in the state on April 23.