ElBaradei was initially tipped to lead the cabinet but his nomination was rejected by the Salafist Al-Nour party.
Beblawi now faces the daunting task of trying to reunite a deeply divided country and rescue its battered economy.
The head of the party added that it was still studying ElBaradei's appointment.
The Muslim Brotherhood, meanwhile, is refusing to recognise the caretaker president or any of his decisions.
Shortly after the Islamist parties made their statements, Egypt's army chief went on Egyptian state media to say that the military will not accept political "maneuvering".
Defense Minister Abdel-Fattah el-Sissi said on Tuesday that "the future of the nation is too important and sacred for maneuvers or hindrance, whatever the justifications".
The blueprint unveiled by Mansour is intended to replace the controversial Islamist-drafted constitution which he suspended following last week's coup.
A committee will be set up to make final improvements to the draft before it is put to a referendum.
Parliamentary elections will then follow within three months and Mansour will announce a date for a presidential election once the new parliament has convened.
Both Beblawi and ElBaradei are well-known on Egypt's political scene.
Beblawi, 76, studied in Cairo and Paris, where he obtained a doctorate in economics.
During his long career, he worked in public and private institutions, both at home and abroad, including as head of Egypt's Export Development Bank between 1983 and 1995.
Egypt's interim president has named liberal economist Hazem el-Beblawi, a former finance minister, as the country's new prime minister, the presidential spokesman, Ahmed al-Muslimani, said.
Liberal opposition chief and Nobel Peace laureate Mohamed ElBaradei was named vice president for foreign relations, Muslimani said on Tuesday.
The appointments come almost a week after the military overthrew Islamist president Mohamed Morsi and chose chief justice Adly Mansour to head the Arab world's most populous country.
He has also taught at several universities around the world and has written numerous books and articles on finance in Arabic, French and English.
Beblawi was appointed as deputy prime minister and finance minister in the "Revolution Cabinet" after a popular uprising saw the ouster of long-time President Hosni Mubarak.
Egypt's military council rejected the Beblawi's resignation in October of 2011, when he quit in protest over deadly clashes that left at least 26 people dead.
ElBaradei, who has the backing of the June 30 Front (an amalgam of several groups opposing Morsi) is widely respected in Egypt and has received the country's highest honour, the Nile Shas, in 2006.
The former director of the UN nuclear watchdog agency, 71, has had a long career on the international scene.
ElBaradei served as an Egyptian diplomat to the United Nations and later as an aide to Egypt's foreign minister. He was the director general of the International Atomic Energy Agency for nearly 12 years. He and the IAEA shared the Nobel Peace Prize in 2005.
ElBaradei was tipped to be the new deputy prime minister last week, but Egyptian media later negated the reports.
http://www.aljazeera.com/news/middleeast/2013/07/20137914354306499.html
