Mr Jebali told reporters in Tunis that he would quit if his efforts failed.
He first made the proposal on Wednesday after the killing of opposition leader Chokri Belaid triggered protests. But his Islamist Ennahda party has opposed the plan for a non-partisan cabinet.
Meanwhile Ennahda supporters attended a rally in the capital, Tunis, a day after Mr Belaid's funeral.
Opposition supporters have blamed the governing party for his assassination - an accusation it denies.
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Tunisia in the Arab Spring
Dec 2010: Trader Mohammad Bouazizi sets himself on fire in Sidi Bouzid, sparking anti-government protests, and later dies
Jan 2011: Zine al-Abedine Ben Ali stands down as president after escalating protests and clashes
March 2011: New technocratic government announced by interim president
Oct 2011: Tunisians vote in first elections of Arab Spring
Dec 2011: Ex-dissident Moncef Marzouki chosen as president, with Ennahada's Hamadi Jebali as PM
May 2012: Salafi Islamists clash with police amid a row over alcohol sales
June 2012: Mr Ben Ali is sentenced to life in prison over the killing of protesters in the 2011 revolution. Saudi Arabia refuses extradition
Feb 2013: Opposition politician Chokri Belaid shot dead; PM announces plans for technocratic government, a move rejected by Ennahada.
The opposition has called for the government to stand down and four groups - including Mr Belaid's Popular Front - have pulled out of the constituent assembly, which is controlled by Ennahda.
On Saturday, Mr Jebali said he would "present the team no later than the middle of next week".
"All the ministries will be independent, including the interior, justice and foreign affairs ministries," he is quoted as saying.
"If it is accepted... I will continue to carry out my duties as head of the government. Otherwise, I will ask the president of the republic to find another candidate to form a new government."
On Wednesday, Mr Jebali announced he would dismiss the current cabinet and form a government of "competent nationals without political affiliation".
Ennahda said the prime minister "did not ask the opinion of his party".'We are Muslims'
Meanwhile Ennadha organised a rally in Tunis to defend legitimacy of the constituent assembly.
Ennahda demonstrators and more conservative Salafi Muslims congregated on the steps of the National Theatre and marched down the main Bourguiba Avenue, the BBC's Wyre Davies reports from Tunis.
Mr Jebali is deeply at odds with his own Ennahda partyGroups of protesters were chanting: "We are Muslims, we will not be moved."
This is a critical time for Tunisia as Islamist parties on the one hand and liberal, secular groups on the other are divided in their views on how the country should develop, our correspondent says.
With pro- and anti-government protests almost daily, a compromise is long overdue, he adds.
Mr Belaid's killing was the first political assassination in Tunisia since the Arab Spring uprising in 2011 and has sparked angry protests across Tunisia.
One police officer has been killed and 59 injured in rallies Wednesday, the Tunisian interior ministry said.
Police have also detained about 375 protesters, the ministry added.
Saturday's rally came a day after Mr Belaid's funeral brought as many as a million mourners onto the streets of the capital.
Mr Belaid, a lawyer and secular political figure, was shot by a gunman as he left home for work. The previous day he had accused a faction inside Ennahda of being behind attacks on the opposition.
Speaking to BBC Arabic after the funeral, Mr Belaid's widow said she would file a lawsuit against the party's leader, Rachid Ghannouchi.
Mr Ghannouchi has condemned the murder and denied any involvement. The government has blamed opponents of democracy.
