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.
- 03/09/2014 EU minister: Turkey to embark on fast train on EU process
- 03/09/2014 Main Prosecutor's Office of Georgia made a statement in connection with the detention of Mikhail Saakashvili in Greece
- 02/09/2014 New sanctions against Russia - EU plans to respond in "strongest possible way"
- 02/09/2014 Merkel addresses parliament on weapon deliveries to Iraq
- 02/09/2014 Netherlands joins new NATO mission to Afghanistan
- 01/09/2014 Rescue operation continues after Paris building blast
- 31/08/2014 Slovakia says it may veto new EU sanctions against Russia
- 31/08/2014 European Parliament to send observers to elections in Ukraine
- 31/08/2014 EU leader call for stronger sanctions against Russia
- 31/08/2014 Mogherini of Italy appointed EU foreign policy chief
- 30/08/2014 Tusk elected new president of Council of Europe
- 30/08/2014 Finnish Prime Minister: “EU leaders won't set new sanctions on Russia”
- 30/08/2014 Leaders congratulate Turkey's new PM
- 30/08/2014 Iranian student ordered to leave Norway
- 30/08/2014 Oslo mayor regrets using illegal labor
- 30/08/2014 UN Security Council calls for protection of humanitarian personnel
- 30/08/2014 Turkey, Germany ministers discuss spying claims
- 29/08/2014 Poland, Ukraine bar overflight by Russian defence minister's plane
- 29/08/2014 OSCE advance team arrives in Mariupol, starts monitoring
- 29/08/2014 Turkey's new government announced
- 29/08/2014 Police chief of Armenia’s Artik city misappropriates large quantities of food and cigarettes under guise of assisting army
- 29/08/2014 First human trials of Ebola vaccine to start next week
- 29/08/2014 EU expresses concerns over economic confidence falling in August
- 28/08/2014 U.S. air strikes on Syria would face formidable obstacles
- 28/08/2014 Sweden authorizes NATO troops to enter its territory
- 28/08/2014 Recep Tayyip Erdogan officially takes office as 12th Turkish president - PHOTOSESSION - UPDATED
- 28/08/2014 Switzerland convenes urgent OSCE Permanent Council meeting on Ukraine
- 28/08/2014 Danish military to combat against ISIL in Iraq
- 28/08/2014 Germany to decide on military aid for Iraq on Sunday: minister
- 28/08/2014 French FM dismisses claims of Turkish support to IS
- 27/08/2014 Putin, Merkel speak for soonest possible termination of bloodshed in Ukraine
- 27/08/2014 Air France urged to halt flights to Ebola-stricken Freetown
- 27/08/2014 Turkey’s ruling party elects Davutoğlu as new chair
- 27/08/2014 EU offered Ukraine and the RF to reach the agreement on gas, without the Stockholm court
- 27/08/2014 Obama says eradicating Islamic State will not be easy
- 27/08/2014 Latvia to hold military exercises, to be joined by 1000 foreign forces
- 27/08/2014 252 arrested during Notting Hill Carnival
- 27/08/2014 NATO chief welcomes last ISAF command handover
- 26/08/2014 Rasmussen: ‘NATO does not recognize the election held in Abkhazia’
- 25/08/2014 Swiss economy minister postpones visit to Russia over situation in Ukraine