Sirisena on Friday night sacked Wickremesinghe and appointed former strongman Mahinda Rajapaksa as the new prime minister. Next day, Sirisena suspended parliament till November 16 after Wickremesinghe sought an emergency session to prove his majority.
The president also withdrew Wickremesinghe's personal security and vehicles in order to accord them to his 72-year-old successor, who staged a dramatic political comeback on Friday.
Jayasuriya said a prorogation of parliament should be one in consultation with the speaker.
"In this context continuing the prorogation of parliament until November 16 will have serious and undesirable consequences for our country and I kindly request you to reconsider same. I consider it is my duty to draw your attention to the convention that a prorogation should be one in consultation with the speaker," Jayasuriya said.
The speaker also questioned Sirisena's decision to withdraw the security of Wickremesinghe.
Jayasuriya reminded Sirisena of certain forcible takeovers of state institutions since Rajapaksa was named Wickremesinghe's successor by the president.
Sirisena's decision to suspend the parliament until November 16 was seen as an effort to coerce legislators into supporting Rajapaksa.
One such crossover was reported this morning as Wadivel Suresh, an Indian Tamil origin UNP legislator from the central tea plantations, pledged support to Rajapaksa.
He was the second UNP legislator to back Rajapaksa since Friday night.
Analysts said Rajapaksa now has 99 seats, 14 short of the 113 required. Wickremesinghe's UNP now stands at 105, just eight short of the majority.
Two parties, the Marxist JVP with their six seats and the main Tamil party, Tamil National Alliance (TNA) with their 16 are to stay neutral.
The TNA sources said Rajapaksa had spoken to the TNA leader R Sampanthan over the telephone and asked for their support.
TNA is reportedly considering two issues; which party should be capable of bringing in a new Constitution to the country addressing Tamil political grievances and which government would deliver the accountability mechanisms outlined in the UN human rights council resolutions on Sri Lanka's human rights accountability during the final phase of the war with the Liberation Tigers of Tamil Eelam (LTTE).
Wickremesinghe, who termed his shock dismissal as illegal and unconstitutional, remained at the prime minister's official residence-cum-office of Temple Trees.
Sirisena and Wickremesinghe had joined to form a government of national unity in 2015 to bring in constitutional and governance reforms including a new constitution to address the long-standing issues if the Tamil minority.
Sri Lanka nearly faced economic sanctions from the West over Rajapaksa' brutal military crackdown on the banned LTTE.
The LTTE sought a separate Tamil homeland in the northern and eastern provinces of the island nation for nearly 30 years before its collapse in 2009 after the Sri Lankan Army killed its supreme leader Velupillai Prabhakaran.
Rajapaksa and his family were facing several cases of corruption and financial irregularities.
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