Mr Somsak Kiatsuranond had made the statement shortly before the 500-seat lower house convened Tuesday morning with the election of the House Speaker and two deputies.
Mr Somsak himself, a long time MP from the northeastern province of Khon Kaen, was elected unanimously in an uncontested vote as new House Speaker.
Fellow party members Charoen Chankomol, MP for Chaiyaphum, were elected First Deputy House Speaker, and Wisut Chaiarun, MP for Phayao, as second deputy House Speaker, respectively.
Next in the process, the secretary-general of the House of Representatives will forward the voting result to the secretary-general of the Cabinet who will propose the selected names for royal endorsement.
Outgoing Prime Minister Abhisit Vejjajiva will respond to the royal command.
Mr Somsak said the Pheu Thai party met earlier to consider Aug 5 as the date of the next House sitting, to vote for the new prime minister, but it depends on when the royal command to appoint the new House Speaker is issued.
"If the royal command is issued August 3 or 4 (Wednesday or Thursday), the voting for the new premier will be on the same date we expect," he said.
Yingluck Shinawatra is almost certain to become the country's first female prime minister. Her Pheu Thai party and its coalition allies hold 300 seats in the House.
The youngest sister of ousted prime minister Thaksin Shinawatra said on Tuesday that her cabinet lineup is half complete, but some positions could change.
"I can't tell how many "outsiders" will take ministerial posts. It's too early to say, more time is needed," said the incoming premier.
Ms Yingluck said it is up to the House Speaker to call lawmakers to convene to select the prime minister, saying she wants the cabinet lineup to be complete as soon as possible so that it can start working to solve the country’s problems.