The leader of the Republic of Macedonia's VMRO-DPMNE party, Nikola Gruevski, could not manage to form a new government by the January 29 deadline, after being mandated 20 days earlier to form an administration.
Albanians make up between one-quarter and one-third of Macedonia's 2.1 million inhabitants, but dominate municipalities in the north and west.
The DUI previously said its presidency was mulling five options - joining a VMRO DPMNE coalition government, joining the main opposition Social Democrats in government, forming a wide-ranging government alliance, staying in opposition, or going for new elections.
Gruevski, who had governed continuously since 2006, all but the first two years in coalition with DUI, stepped down in early 2016 amid uproar over a scandal involving widespread wiretapping of political opponents, judges and other officials.
"Any other solution will only lead to new conflicts and problems in the already divided society, and will not help to reach a sustainable solution or for the implementation of the reform priorities", VMRO-DPMNE said.
DUI spokesman Bujar Osmani said late on Saturday the presidency meeting would continue today.
In addition they are seeking impartial operations and a wider mandate for the Special Prosecution Office (SPO), which is tasked with probing high-level crime, a demand which is not acceptable for VMRO-DPMNE, as some of its senior officials are the subject of SPO investigations.
VMRO-DPMNE leader Nikola Gruevski, prime minister from 2006 to 2016, was handed the mandate on January 9 to form a new government after narrowly winning a December election. We expect political parties to respond to the conditions we have set.
The EU has called on Ivanov to start urgent consultations and select a leader for the forming of as broad a coalition as possible.
This means that Gruevski missed his deadline to secure a majority of at least 61 MPs in the 120-seat parliament and must return his mandate to the President, Gjorge Ivanov, on Monday. The options include giving a mandate to another candidate from the winning party or to Zaev.