Official sources said the cabinet passed the decision at an emergency session on Tuesday to ask for a one-year extension.
The mandate of the 11-month inquiry expires on June 15 but the investigation has run into difficulties, partly due to Syrian reluctance to cooperate and disputes over the veracity of witness statements.
The 15-member Security Council had already extended the mandate of the inquiry for six months in mid-December following an earlier request from the Lebanese government.
An interim report in December implicated senior Syrian officials in the February 2005 killing and criticised Syria for its lack of cooperation with UN investigators.
A follow-up report in March said groundwork had been laid for better cooperation with Damascus, which denies any role in the murder.
Serge Brammertz, the inquiry's chief investigator who took over from German prosecutor Detlev Mehlis in January, interviewed Bashar al-Assad, the Syrian president, last week over the country's alleged role in the assassination.
Lebanon is working with the United Nations to set up an international tribunal to try the suspected assassins.
Four Lebanese ex-security generals have been charged in connection with the crime but no indictments have been issued so far.