Yemen's Cabinet spokesman says the president and rival Shiite rebels are negotiating amid a tense ceasefire, a day after heavy street fighting engulfed the capital, Sanaa, dragging the country into deeper turmoil.

The meeting comes as armed Houthi rebels in pickup trucks mounted with anti-aircraft guns have set up checkpoints across the city and near the prime minister's residence on Tuesday while their fighters are patrolling Sanaa's streets.

The spokesman, Rageh Badi, says President Abed Rabbo Mansour Hadi and a Houthi adviser are discussing possible members of a key commission that will have to fine-tune the outline of Yemen's future federation, as stated in the draft constitution.

Reforming the 85-member commission is long overdue and was part of a U.N.-brokered peace deal following the Houthis' capture of Sanaa in September.