The calls have been made by Bethnal Green & Bow MP Rushanara Ali and Tower Hamlets’ former Olympics ambassador Wais Islam.
The MP has asked Foreign Secretary William Hague to press the Bangladesh government and opposition leaders to “bring an end to the violence.”
She told MPs: “There are real concerns about human rights violations, with the number of dead and injured increasing at an alarming rate.”
Former councillor Wais Islam urged politicians to publicly condemn death sentences issued by a Bangladesh War Crimes tribunal he claims “falls seriously short of international standards and human rights laws.”
He said: “Most Bangladeshis in the East End oppose capital punishment, although they want justice against war crimes.”
The tribunal is being held against alleged war criminals from the 1971 War of Independence when East Pakistan broke away to become the new state of Bangladesh.
But campaigners in east London say the UN does not recognise “the flawed set up” of Dhaka’s tribunal.