According to a press release issued by the Hungarian EU presidency on its web site, Gyori praised Montenegro for being "a stabilising factor in the West Balkans."
"It has good neighbourly relations, and plays an important role in regional cooperation."
In addition, Montenegro has achieved visa liberalisation and concluded the Stability and Association Agreement and has acquired candidate status within 12 months, the Hungarian official added.
Also, "for Montenegro to start the accession talks, it should make progress in consolidating the rule of law and increasing the efficiency of public administration, pass a constitutionally appropriate elections law, and enhance media freedom."
The Hungarian official was quoted as saying that "Montenegro should guarantee the legal status of Croatian, Bosnian and Kosovar refugees and respect their rights."
That southeastern European Adriatic country is expected "to continue the fight against organised crime and corruption."
The 35-page draft resolution reads that the opening of Montenegro's accession negotiations should not be postponed.
Montenegro signed an association agreement with the EU in 2007, and submitted its EU accession application in 2008. The country was awarded candidate status in December 2010, but the EU has still not set a date for starting the accession negotiations.
"The European Council will decide on the matter after Montenegro has duly complied with all expectations, in terms of the rule of law, public administration, and justice," the Hungarian presidency said on its web site.