Singhvi said the MLAs have resigned as they want to avoid disqualification.
The Supreme Court bench, headed by Chief Justice Ranjan Gogoi, gave the Speaker time till July 16 to decide on the resignations and ordered a status quo till then on the resignations and on the question of disqualification.
The Speaker on Thursday evening said he will need time to decide on whether to accept the resignations, hours after the Supreme Court asked him to take a decision within a day.
His approach assumes significance as the Assembly convened on Friday for a 10-day session.
Till their resignations are accepted, the 16 legislators - 13 of the Congress and 3 of the JD(S) - would be bound by the whip issued by their respective parties regarding their attendance of the Assembly and any voting therein.
And if they violate the whip, they can face disciplinary action, including disqualification, which will bar them from re-election for the remaining period of the Assembly.
Both the Congress and the JD(S) have issued whips to all their legislators to be present in the Assembly for passing the state Budget (finance bill) and participate in the discussions on other subjects till the session ends on February 24.
"The whip has been issued even to the rebels, as their resignations have not been accepted by the Speaker so far," Congress spokesman Ravi Gowda told IANS.
The Congress Legislature Party (CLP) leader Siddaramaiah has already petitioned the Speaker on Monday to disqualify the party lawmakers who defy the whip, irrespective of their status, and skip the session.
The rebels, however, claimed that disqualification would not apply to them as they have already resigned from their respective Assembly segments and submitted the letters to the Speaker as well as the Governor on July 6.
In the 225-member Assembly, including one nominated, the Congress has 79 MLAs, including Speaker, and JD(S) has 37. Lone members of BSP and KPJP (a regional outfit) besides an Independent also were with the government, taking their tally to 118, five more than the required majority mark.
If the Speaker accepts all the 16 resignations, the Assembly's effective strength will drop to 209 from 225 and the ruling coalition will be reduced to 100, when the halfway mark would be 105.
Besides the 16 MLAs of the Congress and the JD(S), the KPJP legislator and the Independent have also withdrawn their support to the government.
On the other hand, the BJP has 105 MLAs and is eyeing to form the government.
As the Assembly convened on Friday, Chief Minister H D Kumaraswamy said he was ready to seek trust vote to prove that his JD(S)-Congress coalition government has majority in the House.
Kumaraswamy said he was ready to face even a No-Confidence Motion if the BJP wants to move it in the Assembly.
He asked the Speaker to fix a date and time to move the Confidence Motion in the House.
"I leave it to you to decide if I should seek trust-vote or face no-confidence motion on the floor of this House when you fix the date and time," the chief minister told the Speaker in Kannada.
The first day of the session was adjourned without transaction of any business after some obituary references.
Kumaraswamy's act of bravado came soon after the Supreme Court gave the Speaker time till July 16 to decide on the resignations of the 10 rebel legislators of the ruling parties who re-submitted them to him on Thursday here.
"I can continue as Chief Minister after the floor test in view of the prevailing political situation caused by the spate of resignations by some of our legislators," added Kumaraswamy.
The 10 rebels -- 7 of the Congress and 3 JD(S) -- petitioned the apex court on July 10 that the Speaker was allegedly delaying acceptance of their resignations they submitted in his office on July 6.
The Speaker, however, said on July 9 that of the 13 resignations his office received, as 8 were not in the prescribed format, he asked them to re-submit by July 11.
Six more Congress lawmakers also resigned but did not go to the top court against the speaker.
Directing the Speaker to maintain status quo on the rebels' plea, the three-judge bench of the top court headed by Chief Justice Ranjan Gogoi said they (rebels) will remain legislators and would not be disqualified.
The Congress and JD(S) have also petitioned the Speaker to disqualify the 10 rebels who went to the apex court against him for defying their whip in attending their respective legislature party meetings.
The top court gave additional time to the Speaker in response to his petition to modify its Thursday's order to decide on the resignations by Friday.