So far Dr Jaafari has given little sign of wanting to accommodate the Sunni insurgency.
Walters also e-mailed a professor at Columbia University Graduate School of Journalism on Jaafari's behalf.
Sheherazad Jaafari said that she gained admission to Columbia based on her own qualifications.
Walters has said that Jaafari was "looking for a job" when she contacted her.
But a large bloc of Kurds, Sunni Arabs and secular politicians have been forcefully opposed to Jaafari.
Opposition to al-Jaafari has been growing, and the Shiite coalition is being pressured to reconsider its decision.
Mr Jaafari agreed to step aside to make way for a more effective Shia politician, Jawad al-Maliki.
ECONOMIST: Now everything depends on America keeping its nerve
The Kurds say that they simply have no faith that Mr Jaafari will act on his commitments.
If Dr Jaafari keeps him on, many Sunnis would find it hard to serve in the same team.
Jaafari also said the government is expecting armed opposition groups to end violence.
Rather than representing a united Iraq, the UIA is now mainly a religious Shia grouping that includes Mr Jaafari.
ECONOMIST: Iraq takes another step down a long, hard road | The
Both the Sunni and Kurdish factions want the Shiite alliance to replace candidate Ibrahim al Jaafari with someone else.
The whole point is that the Shiite politicians are debating whether to keep Ibrahim al-Jaafari as their nomination for prime minister.
Jaafari himself says he is attracted by the "Turkish model" in which the army acts as a bulwark of the republic.
The country's transitional prime minister, al-Jaafari has been a polarizing figure since the Shiite-dominated United Iraqi Alliance nominated him two months ago.
"And thusfar, Jaafari has not been able to do that, " she said.
Syria's U.N. ambassador, Bashar Jaafari, called the resolution a "piece of theater" that serves the interests of other countries in the region.
In New York, Sheherazad Jaafari, daughter of Syrian Ambassador to the U.N.
Now, Mr Jaafari will try again to put together an effective government.
ECONOMIST: Iraq's Shias stick with the devil they know | The
Mr Jaafari has called the situation unacceptable and promised a full investigation.
ECONOMIST: Iraq takes another step down a long, hard road | The
Dr Jaafari, back from exile in London, is struggling to regain control.
Ibrahim al-Jaafari, a former prime minister, hankers after a return to office.
On Friday, the Shiite-led political bloc, the United Iraqi Alliance, put forward al-Maliki of the Dawa Party as its candidate to replace al-Jaafari.
Almost certainly, Mr Talabani will be Iraq's president and Dr Ibrahim al-Jaafari, who heads the Dawa party within the Shia alliance, prime minister.
Jaafari reiterated "again and again and again" his government's commitment to a peace plan and said Syrian troops had withdrawn from cities and towns.
Jalal Talabani, the Kurdish leader, has led a campaign to force the Alliance to rescind its decision to re-nominate Ibrahim al-Jaafari as prime minister.
Iraqi Prime Minister Ibrahim al-Jaafari has launched an immediate investigation, and acting Human Rights Minister Nermin Othman Hassan said other probes also had begun.
Syrian Ambassador Bashar Jaafari objected to the draft treaty's failure to include an embargo on transferring arms to "terrorist armed groups and to non-state actors".
Bashar Jaafari, Syria's ambassador to the United Nations, told reporters Thursday that armed groups had eight violations of the cease-fire that resulted in several deaths Thursday.
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