Gruevski made the remarks at a news conference held here jointly with his Hungarian counterpart Viktor Orban.
Gruevski said his country had met all EU accession conditions and was ready to negotiate the entry, but was being held back because of a dispute with Greece, essentially over his country's name.
The Balkans could not become a stable region until Macedonia had been admitted to the EU and NATO and Hungary is committed to stability in Southeast Europe, Orban said at the news conference.
He agreed with Gruevski that resolution of Macedonia's name dispute with Greece should not be a prerequisite for starting EU accession talks.
The dispute had to be resolved, he said, but he suggested that resolution should become part of the EU negotiations rather than a condition for getting them going.
Macedonia has been an EU candidate since 2005, but the EU Council has not yet set a date for opening accession talks.
The country's EU aspirations have been blocked by Greece, which says that the name of Macedonia implies territorial claims against its northern province bearing the same name.
Greece also vetoed Macedonia's admission to NATO in 2008.
On bilateral ties between Hungary and Macedonia, Orban said there were significant untapped opportunities for economic cooperation. The two sides were setting up a joint economic commission, which will meet in January next year, he added.
Gruevski also had meetings with Hungarian President Janos Ader and Speaker of Parliament Laszlo Kover.
- 03/09/2015 Four Turkish police officers killed in PKK bomb attack
- 03/09/2015 Hundreds of migrants on tracks at Calais block trains to UK
- 03/09/2015 Greece's Syriza party falls behind conservatives in latest poll
- 02/09/2015 Germany pushes for a common EU asylum policy
- 02/09/2015 NATO activates six headquarters in eastern Europe
- 02/09/2015 Turkish parliament to discuss Syria & Iraq mandate
- 02/09/2015 EU decides to extend anti-Russian sanctions until March 2016
- 02/09/2015 Ex-IS hostage to run for parliament in Turkey
- 02/09/2015 2 Turkish troops injured in Sirnak base attack
- 02/09/2015 Tusk says EU has to do more on migrant crisis
- 01/09/2015 Migrants protest as Hungary shutters Budapest train station
- 01/09/2015 19 civilians killed in terror attacks in 56 days in Turkey
- 01/09/2015 Turkey: 3 foreign journalists arrested on terror charges
- 01/09/2015 4 missing, 4 injured after explosion in Spain fireworks factory
- 01/09/2015 Policeman, civilian injured in southeast Turkey attack
- 30/08/2015 17-year-old migrant killed in shootout at sea with Greek police
- 30/08/2015 European ministers agree more railway security, urge Schengen changes
- 30/08/2015 Three refugee children found critically ill in Austria
- 29/08/2015 Turkish planes join anti-IS coalition in Syria raid for first time
- 29/08/2015 Former deputy interior minister of Georgia shot
- 29/08/2015 Turkey: 24 people injured in Mardin bomb attack
- 29/08/2015 Croatia comes out of crisis: PM
- 29/08/2015 Deadly attack in eastern Turkey
- 28/08/2015 PKK have killed 14,000 since 1984
- 28/08/2015 Turkey: PM Davutoglu unveils interim Cabinet
- 28/08/2015 NATO’s support for sovereignty and territorial integrity is strong, says secretary general
- 28/08/2015 2 French journalists held for 'attempted blackmail of Morocco king'
- 28/08/2015 Tusk says EU, Ukraine want to see early free travel
- 27/08/2015 Greece to use EU money to open refugee centres
- 27/08/2015 Dozens found dead in truck on Austrian highway
- 27/08/2015 Opening of NATO training center in Georgia to destabilize region: Russian Foreign Ministry
- 27/08/2015 NATO opens training center in Georgia
- 27/08/2015 Hungary migrant crisis escalates as police fire tear gas
- 27/08/2015 Italy, Spain, US troopers take part in Romania NATO drill
- 27/08/2015 PKK terrorists attack Turkish police; there are wounded
- 27/08/2015 First opposition member joins Turkey's interim Cabinet
- 26/08/2015 Greek president expected to call election on Friday
- 25/08/2015 At least three dead in shootout in northern France
- 25/08/2015 Hollande, Ban Ki-Moon urge efforts for reaching binding accord on Paris climate summit
- 25/08/2015 Merkel to visit protest-hit refugee home