A group of Jatiya Party MPs led by Kazi Firoz Rashid, a member of the party's presidium, delivered the letter to the speaker's office.
Jatiya Party is currently represented by 25 members of parliament, including the reserved seats for women.
But the party's Rangpur-3 seat was vacated after the death of its chairman HM Ershad and is slated to be contested in a by-election on Oct 5.
The letter was handed to officials at the speaker's office as Shirin Sharmin is currently abroad.
Her secretary Kamal Billah confirmed receipt of the letter to bdnews24.com.
But Jatiya Party leaders, including Kazi Firoz, remained tight-lipped on the matter.
"I don't want to say anything about this issue," Jatiya Party MP Shamim Haider Patwary, also a party presidium member, told bdnews24.com.
Another Jatiya Party presidium member and MP Shariful Islam Jinnah said, "The party's secretary general and chief whip in parliament Moshiur Rahman Ranga will address the issue."
But Ranga did not take bdnews24.com's phone calls for comment.