The party has already written to the speaker, asking him to hold a parliamentary session immediately.
The UNF, JVP and the TNA too, have made similar requests to the speaker.
All these written requests have the signatures of 128 MPs.
Meanwhile, UNP leader Ranil Wickremesinghe told the media that the speaker has the powers to summon parliament.
Earlier in the day, speaker Jayasuriya called on the Maha Nayake Theras of the Malwatte and Asgiriya Chapters in Kandy.
He told the top prelates that their guidance was important to positively resolve the political stalemate, noting that the present dispute should be solved democratically within parliament, instead of resorting to street fights.
The speaker stressed that he did not want to appear for anyone, and said his intention was to support parliament to resolve the dispute peacefully for the sake of the country and the people.
He warned the violent developments that have already claimed two lives could result in a major diplomatic and economic setback for the country.
Jayasuriya called on the Maha Nayake Theras to remind all party leaders about their responsibility to summon parliament and act democratically by respecting the majority opinion.