But UN diplomats in New York said on Thursday the UN's chief investigator into al-Hariri's killing, Detlev Mehlis, planned to leave the job by the end of the year.
He had been appointed in May to lead the inquiry into the 14 February truck bombing which killed the former prime minister in Beirut.
Mehlis intends to submit a report to the Security Council on 12 December, after which he will speak to the 15-nation body as his last official UN task, Council diplomats said.
Ibrahim Gambari, the UN undersecretary-general for political affairs, had said he expected the investigation to continue but that Mehlis may hand over the work to someone else.
"The government agreed to ask the United Nations to extend the mandate of the inquiry for six months," Lebanese Defence Minister Elias Murr said after a weekly cabinet session.
But the government failed to agree on calling for an international trial for any suspects, with pro-Syrian Shia Muslim ministers firmly opposing any such move.
"If he (Mehlis) wants to indict anyone, the indictment should go to Syria and through the Syrian legal process"
Syrian Deputy Prime Minister
Mehlis' interim report in October cast suspicion on senior Syrian officials and suggested the assassination was planned by top security officials in Damascus and their Lebanese allies.
The UN team is set to quiz five Syrian officials in Vienna next week in connection with the murder.
The Security Council has told Syria to cooperate with the investigation or face the prospect of further action, which could lead to sanctions. Syria has denied the accusations and called the Mehlis report politically motivated.
The death of al-Hariri, a strong opponent of Syrian domination of Lebanon, transformed Lebanon's political landscape, leading to an anti-Syrian outcry that forced Syria to pull its troops out of Lebanon after three decades.
Syria has recently stepped up its campaign against Mehlis' initial findings after a Syrian witness said he gave a false testimony implicating Syrians.
Mehlis said in remarks published in the Lebanese press on Thursday that his investigation had not been undermined by Syrian witness Hosam Taher Hosam, who recanted his testimony.
Hosam appeared on Syrian television this week to accuse Lebanese officials of an elaborate scheme of threats, bribery and torture to induce him to testify falsely against Syria and said the inquiry's initial findings rested largely on his lies.
"I'm used to this kind of propaganda," Mehlis was quoted by as-Safir daily as saying. "I've spent 40 years in Germany and we used to see such things in former eastern European countries."
Detlev Mehlis (L) is heading the
UN probe into al-Hariri's killing
Mehlis said he might seek to question more Syrian officials after the five are quizzed in Vienna next week. Syria's Deputy Prime Minister Abdullah al-Dardari said on Thursday Damascus might eventually hand over to the United Nations any of its nationals indicted for the assassination, but only after indictments had gone through a Syrian legal process.
"If he (Mehlis) wants to indict anyone, the indictment should go to Syria and through the Syrian legal process," he told reporters in London. "The person will be arrested by Syrian authorities and then handed over to the UN"
The "Vienna five" have not been named, but diplomats said those going would include Lieutenant General Rustom Ghazali, Syria's former military intelligence chief in Lebanon.
Dardari said the five Syrians will have their lawyers with them under a deal he said was guaranteed by Russia.
Russian involvement, Dardari argued, would make it hard for the Security Council to press for sanctions against Syria when Mehlis submits his final report on 15 December.
"It's not going to be very easy to say Syria is not cooperating without any evidence (of that)," he said.
"So I don't think the Security Council will...raise the stakes towards sanctions on 15 December," he added, predicting that prospects for sanctions would recede further as Syria is seen to be cooperating with the UN investigation.